Thread: dw/dt how to solve by two methods

I'm not really sure how to do this at all. My professor didn't really go over this that well and this is one of the few topics I don't understand on tomorrow's Calc III exam.

Find dw/dt by two methods and compare the results when t = 1
w=sqrt(z)-y/x, where x = 2t, y =3t and z = e^2t

so im sure that i take the partial derivs and then what?

is it all over x or just y/x

Originally Posted by radioheadfan

I'm not really sure how to do this at all. My professor didn't really go over this that well and this is one of the few topics I don't understand on tomorrow's Calc III exam.

Find dw/dt by two methods and compare the results when t = 1
w=sqrt(z)-y/x, where x = 2t, y =3t and z = e^2t

so im sure that i take the partial derivs and then what?

Method(1): Apply the multivariable functions' chain rule.
Method(2): Substitute the values of x,y & z in w to make w a function in t, and differentiate it as you did in CalcI.

The best way to do this is take the partial derivates of the original function. Then take the derivatives of x,y,z.

After figuring both of these out then all you have to do is apply the chain rule so you get

I did the problem out and got e as the final answer. Correct me if im wrong please.

(3t/(2t)^2 x2) +(- 1/2t x 3) + (2e^2t/2sqrt(e^2t)) and after plugging in and simplifying i got e. If im wrong show me how i went wrong please.