Use the chain rule...

[OrangeOne]

Look at the function f(x,y)= e[supniozw3t]x^2*y[/supniozw3t] + xy and the following compound function:

u(t)= f(cos t,sin t)

Determine u'(t) with the help from the chain rule...


Help is needed and very appreciated!!

 

[Deleted member 4993]

Look at the function f(x,y)= e[sup:2viadhxn]x^2*y[/sup:2viadhxn] + xy and the following compound function:

u(t)= f(cos t,sin t)

Determine u'(t) with the help from the chain rule...


Help is needed and very appreciated!!

This is a straight-forward problem.

du/dt = df/d(cost) * d(cost)/dt + df/d(sint) * d(sint)/dt

f(cost, sint) = e^(cos^2t * sint) + cost * sint

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[OrangeOne]

Cheers,

I dont understand how to find the derivative for e^(cos^2t*sin t)

I get: cos^2t*sin t * e*(cos^2t*sin t)* (-sin^2t*sin t*cos^2t*cos t) but something tells me this is wrong....

 

[Deleted member 4993]

Cheers,

I dont understand how to find the derivative for e^(cos^2t*sin t)

I get: cos^2t*sin t * e*(cos^2t*sin t)* (-sin^2t*sin t*cos^2t*cos t) but something tells me this is wrong....

To find

\(\displaystyle \frac{d}{dt}\left (e^{cos^2(t)*sin(t)\right)\)

substitute

\(\displaystyle p \ = \cos^2(t) \cdot sin(t)\)

\(\displaystyle \frac{dp}{dt} \ = \ 2 * cos(t) * [-sin(t)] * sin(t) + cos^2(t) * cos(t)\)

\(\displaystyle \frac{d}{dt}\left (e^p\right) \ = \ e^p * \frac{dp}{dt}\)

Now put all these together....