Trouble taking derivative
$$p(x) = frac{RTx}{1-bx} -ax^2$$
If $R$ and $T$ are constants, how can I find the derivative of this?
What I obtained:
$p'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}bRTx - 2ax$
Is this correct?
Thanks!
derivatives
add a comment |
$$p(x) = frac{RTx}{1-bx} -ax^2$$
If $R$ and $T$ are constants, how can I find the derivative of this?
What I obtained:
$p'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}bRTx - 2ax$
Is this correct?
Thanks!
derivatives
1
If you show your steps someone could advise you better. To me it doesn't look like you used the quotient rule on first term.
– coffeemath
Nov 27 at 1:03
1
Almost correct, but not quite. In executing the product rule on the first term, note that the derivative of $(1-xb)^{-1}$ is $$(-1)(-b)(1-xb)^{-2} = b(1-xb)^{-2}$$ per the chain rule. So you wouldn't have that $RTx$ in the second term of your expression - just $RT$ - and the sign of the term would be positive (not negative).
– Eevee Trainer
Nov 27 at 1:03
add a comment |
$$p(x) = frac{RTx}{1-bx} -ax^2$$
If $R$ and $T$ are constants, how can I find the derivative of this?
What I obtained:
$p'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}bRTx - 2ax$
Is this correct?
Thanks!
derivatives
$$p(x) = frac{RTx}{1-bx} -ax^2$$
If $R$ and $T$ are constants, how can I find the derivative of this?
What I obtained:
$p'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}bRTx - 2ax$
Is this correct?
Thanks!
derivatives
derivatives
edited Nov 27 at 1:32
Eevee Trainer
4,090530
4,090530
asked Nov 27 at 0:57
M Do
124
124
1
If you show your steps someone could advise you better. To me it doesn't look like you used the quotient rule on first term.
– coffeemath
Nov 27 at 1:03
1
Almost correct, but not quite. In executing the product rule on the first term, note that the derivative of $(1-xb)^{-1}$ is $$(-1)(-b)(1-xb)^{-2} = b(1-xb)^{-2}$$ per the chain rule. So you wouldn't have that $RTx$ in the second term of your expression - just $RT$ - and the sign of the term would be positive (not negative).
– Eevee Trainer
Nov 27 at 1:03
add a comment |
1
If you show your steps someone could advise you better. To me it doesn't look like you used the quotient rule on first term.
– coffeemath
Nov 27 at 1:03
1
Almost correct, but not quite. In executing the product rule on the first term, note that the derivative of $(1-xb)^{-1}$ is $$(-1)(-b)(1-xb)^{-2} = b(1-xb)^{-2}$$ per the chain rule. So you wouldn't have that $RTx$ in the second term of your expression - just $RT$ - and the sign of the term would be positive (not negative).
– Eevee Trainer
Nov 27 at 1:03
1
1
If you show your steps someone could advise you better. To me it doesn't look like you used the quotient rule on first term.
– coffeemath
Nov 27 at 1:03
If you show your steps someone could advise you better. To me it doesn't look like you used the quotient rule on first term.
– coffeemath
Nov 27 at 1:03
1
1
Almost correct, but not quite. In executing the product rule on the first term, note that the derivative of $(1-xb)^{-1}$ is $$(-1)(-b)(1-xb)^{-2} = b(1-xb)^{-2}$$ per the chain rule. So you wouldn't have that $RTx$ in the second term of your expression - just $RT$ - and the sign of the term would be positive (not negative).
– Eevee Trainer
Nov 27 at 1:03
Almost correct, but not quite. In executing the product rule on the first term, note that the derivative of $(1-xb)^{-1}$ is $$(-1)(-b)(1-xb)^{-2} = b(1-xb)^{-2}$$ per the chain rule. So you wouldn't have that $RTx$ in the second term of your expression - just $RT$ - and the sign of the term would be positive (not negative).
– Eevee Trainer
Nov 27 at 1:03
add a comment |
3 Answers
3
active
oldest
votes
$$p(x) = frac{RTx}{1-bx} -ax^2=(RTx)(1-bx)^{-1}-ax^2$$
begin{align}p'(x)&=(RT)(1-bx)^{-1}+(RTx)(-1)(1-bx)^{-2}(-b)-2ax \
&=(RT)(1-bx)^{-1}+(bRTx)(1-bx)^{-2}-2axend{align}
add a comment |
I would say you should simplify a little bit more.
$f'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}(-b)(RTx)- 2ax\
RT(1-xb)^{-2}(1-xb + xb) - 2ax\
frac {RT}{(1-xb)^2}-2ax$
add a comment |
Use the quotient rule: ($frac {f(x)}{g(x)} = frac {f'(x)g(x) - f(x)g'(x)}{g^2(x)}$)
the sum rule: ($(f(x) + g(x))' = f'(x) + g'(x)$.)
constant rule: ($(af(x))' = af'(x)$)
And power rule: ($[x^k]' = kx^{k-1}$)
And the entire thing is simple:
$p(x) = frac{RTx}{1-bx} -ax^2$ so
$p'(x) = frac{[RTx]'(1-bx) -RTx[1-bx]'}{(1-bx)^2} -[ax^2]'=$
$ frac {RT(1-bx)-RTx(-b)}{(1-bx)^2} - 2ax=$
$frac {RT - RTbx + RTxb}{(1-bx)^2} -2ax = frac {RT}{(1-bx)^2} - 2ax$.
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3015174%2ftrouble-taking-derivative%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$$p(x) = frac{RTx}{1-bx} -ax^2=(RTx)(1-bx)^{-1}-ax^2$$
begin{align}p'(x)&=(RT)(1-bx)^{-1}+(RTx)(-1)(1-bx)^{-2}(-b)-2ax \
&=(RT)(1-bx)^{-1}+(bRTx)(1-bx)^{-2}-2axend{align}
add a comment |
$$p(x) = frac{RTx}{1-bx} -ax^2=(RTx)(1-bx)^{-1}-ax^2$$
begin{align}p'(x)&=(RT)(1-bx)^{-1}+(RTx)(-1)(1-bx)^{-2}(-b)-2ax \
&=(RT)(1-bx)^{-1}+(bRTx)(1-bx)^{-2}-2axend{align}
add a comment |
$$p(x) = frac{RTx}{1-bx} -ax^2=(RTx)(1-bx)^{-1}-ax^2$$
begin{align}p'(x)&=(RT)(1-bx)^{-1}+(RTx)(-1)(1-bx)^{-2}(-b)-2ax \
&=(RT)(1-bx)^{-1}+(bRTx)(1-bx)^{-2}-2axend{align}
$$p(x) = frac{RTx}{1-bx} -ax^2=(RTx)(1-bx)^{-1}-ax^2$$
begin{align}p'(x)&=(RT)(1-bx)^{-1}+(RTx)(-1)(1-bx)^{-2}(-b)-2ax \
&=(RT)(1-bx)^{-1}+(bRTx)(1-bx)^{-2}-2axend{align}
answered Nov 27 at 1:09
Siong Thye Goh
99k1464116
99k1464116
add a comment |
add a comment |
I would say you should simplify a little bit more.
$f'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}(-b)(RTx)- 2ax\
RT(1-xb)^{-2}(1-xb + xb) - 2ax\
frac {RT}{(1-xb)^2}-2ax$
add a comment |
I would say you should simplify a little bit more.
$f'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}(-b)(RTx)- 2ax\
RT(1-xb)^{-2}(1-xb + xb) - 2ax\
frac {RT}{(1-xb)^2}-2ax$
add a comment |
I would say you should simplify a little bit more.
$f'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}(-b)(RTx)- 2ax\
RT(1-xb)^{-2}(1-xb + xb) - 2ax\
frac {RT}{(1-xb)^2}-2ax$
I would say you should simplify a little bit more.
$f'(x) = RT(1-xb)^{-1} + (-1)(1-xb)^{-2}(-b)(RTx)- 2ax\
RT(1-xb)^{-2}(1-xb + xb) - 2ax\
frac {RT}{(1-xb)^2}-2ax$
answered Nov 27 at 2:05
Doug M
43.9k31854
43.9k31854
add a comment |
add a comment |
Use the quotient rule: ($frac {f(x)}{g(x)} = frac {f'(x)g(x) - f(x)g'(x)}{g^2(x)}$)
the sum rule: ($(f(x) + g(x))' = f'(x) + g'(x)$.)
constant rule: ($(af(x))' = af'(x)$)
And power rule: ($[x^k]' = kx^{k-1}$)
And the entire thing is simple:
$p(x) = frac{RTx}{1-bx} -ax^2$ so
$p'(x) = frac{[RTx]'(1-bx) -RTx[1-bx]'}{(1-bx)^2} -[ax^2]'=$
$ frac {RT(1-bx)-RTx(-b)}{(1-bx)^2} - 2ax=$
$frac {RT - RTbx + RTxb}{(1-bx)^2} -2ax = frac {RT}{(1-bx)^2} - 2ax$.
add a comment |
Use the quotient rule: ($frac {f(x)}{g(x)} = frac {f'(x)g(x) - f(x)g'(x)}{g^2(x)}$)
the sum rule: ($(f(x) + g(x))' = f'(x) + g'(x)$.)
constant rule: ($(af(x))' = af'(x)$)
And power rule: ($[x^k]' = kx^{k-1}$)
And the entire thing is simple:
$p(x) = frac{RTx}{1-bx} -ax^2$ so
$p'(x) = frac{[RTx]'(1-bx) -RTx[1-bx]'}{(1-bx)^2} -[ax^2]'=$
$ frac {RT(1-bx)-RTx(-b)}{(1-bx)^2} - 2ax=$
$frac {RT - RTbx + RTxb}{(1-bx)^2} -2ax = frac {RT}{(1-bx)^2} - 2ax$.
add a comment |
Use the quotient rule: ($frac {f(x)}{g(x)} = frac {f'(x)g(x) - f(x)g'(x)}{g^2(x)}$)
the sum rule: ($(f(x) + g(x))' = f'(x) + g'(x)$.)
constant rule: ($(af(x))' = af'(x)$)
And power rule: ($[x^k]' = kx^{k-1}$)
And the entire thing is simple:
$p(x) = frac{RTx}{1-bx} -ax^2$ so
$p'(x) = frac{[RTx]'(1-bx) -RTx[1-bx]'}{(1-bx)^2} -[ax^2]'=$
$ frac {RT(1-bx)-RTx(-b)}{(1-bx)^2} - 2ax=$
$frac {RT - RTbx + RTxb}{(1-bx)^2} -2ax = frac {RT}{(1-bx)^2} - 2ax$.
Use the quotient rule: ($frac {f(x)}{g(x)} = frac {f'(x)g(x) - f(x)g'(x)}{g^2(x)}$)
the sum rule: ($(f(x) + g(x))' = f'(x) + g'(x)$.)
constant rule: ($(af(x))' = af'(x)$)
And power rule: ($[x^k]' = kx^{k-1}$)
And the entire thing is simple:
$p(x) = frac{RTx}{1-bx} -ax^2$ so
$p'(x) = frac{[RTx]'(1-bx) -RTx[1-bx]'}{(1-bx)^2} -[ax^2]'=$
$ frac {RT(1-bx)-RTx(-b)}{(1-bx)^2} - 2ax=$
$frac {RT - RTbx + RTxb}{(1-bx)^2} -2ax = frac {RT}{(1-bx)^2} - 2ax$.
answered Nov 27 at 3:06
fleablood
68.1k22684
68.1k22684
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3015174%2ftrouble-taking-derivative%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
If you show your steps someone could advise you better. To me it doesn't look like you used the quotient rule on first term.
– coffeemath
Nov 27 at 1:03
1
Almost correct, but not quite. In executing the product rule on the first term, note that the derivative of $(1-xb)^{-1}$ is $$(-1)(-b)(1-xb)^{-2} = b(1-xb)^{-2}$$ per the chain rule. So you wouldn't have that $RTx$ in the second term of your expression - just $RT$ - and the sign of the term would be positive (not negative).
– Eevee Trainer
Nov 27 at 1:03