Calculus chain rule questions

May 2010
6
1
Hi I have a few calculus questions, could you please explain how to get the final answer too, thanks.

Derivative of :






dy/dx here

dy/dx here

dy/dt here








 
Last edited:

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Hi I have a few calculus questions, could you please explain how to get the final answer too, thanks.

Derivative of :

Chain rule of the chain rule with a product rule


chain rule

dy/dx here
chain rule
dy/dx here
product rule with chain
dy/dt here
chain


You haven't attempted much so start by trying that.
 
May 2010
6
1
Ok I figured out the middle three but I cannot quite get the first one and last one
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
\(\displaystyle (cos\big(e^{x^2cos(x)}\big))^{\frac{1}{2}}\)

\(\displaystyle \frac{1}{2}(cos\big(e^{x^2cos(x)}\big))^{\frac{-1}{2}}(-sin\big(e^{x^2cos(x)}\big))(e^{x^2cos(x)}(2xcos(x)-x^2sin(x)))\)

I am not going to simplify that.
 
  • Like
Reactions: KK88

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
\(\displaystyle e^{2sin(8t)}\)

\(\displaystyle 8e^{2sin(8t)}2cos(8t)=16e^{2sin(8t)}cos(8t)\)
 
  • Like
Reactions: KK88
May 2010
6
1
Thanks for the responses.
The second one is correct however I still cant get the first one right, I input this:

 
  • Like
Reactions: Rapha

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
The first one is correct too. Here is the maple output.
 
  • Like
Reactions: KK88

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
\(\displaystyle \frac{1}{2}(cos\big(e^{x^2cos(x)}\big))^{\frac{-1}{2}}(-sin\big(e^{x^2cos(x)}\big))(e^{x^2cos(x)}(2xcos(x)-x^2sin(x)))\)

You need to have this quantity in parenthesis.
(2xcos(x)-x^2sin(x))
 
  • Like
Reactions: KK88