This problem is from an r/calculus thread

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benorin
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Homework Statement:

If $$y=\left( \int_0^x (t^{3}+1)^{10}\, dt\right) ^3$$
Find ##\tfrac{dy}{dx}##

Relevant Equations:

I hope it is ok for me to post here, I just needed ##\LaTeX##. Thank you!

FTC, chain rule, power rule
I hope it is ok for me to borrow this post: No HW help required here. I just wanted to have LaTeX enabled forum to post my answer to this thread in r/calculus

Work: If $$y= \left( \int_0^x (t^{3}+1)^{10}\, dt\right) ^3 $$
then $$\begin{gathered} \tfrac{dy}{dx} =3 \left( \int_0^x (t^{3}+1)^{10}\, dt\right) ^2\cdot \tfrac{d}{dx} \left( \int_0^x (t^{3}+1)^{10}\, dt\right) \quad (1)\\ =\boxed{3 \left( \int_0^x (t^{3}+1)^{10}\, dt\right) ^2\cdot (x^{3}+1)^{10}}\quad (2) \\ \end{gathered}$$

where (1) is power rule followed by the chain rule and (2) is FTC.
 
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  • #4
berkeman
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Homework Statement:: If $$y=\left( \int_0^x (t^{3}+1)^{10}\, dt\right) ^3$$
Find ##\tfrac{dy}{dx}##
Relevant Equations:: I hope it is ok for me to post here, I just needed ##\LaTeX##. Thank you!

FTC, chain rule, power rule

No HW help required here. I just wanted to have LaTeX enabled forum to post my answer to this thread in r/calculus
What's an r/calculus?
 
  • #5
benorin
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What's an r/calculus?
The lower case “r/“ prefix denotes that it’s followed by the name of a subreddit (ie it’s a Reddit forum basically).
 
  • #6
etotheipi
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What's an r/calculus?
To be honest, the only one you really need to know is r/prequelmemes
 
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  • #7
benorin
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Lmao
 

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