# dw/dt how to solve by two methods

• Mar 4th 2010, 05:09 PM
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?
• Mar 4th 2010, 05:12 PM
UODuck1879
is it all over x or just y/x
• Mar 4th 2010, 05:12 PM
Miss
Quote:

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.
• Mar 4th 2010, 05:21 PM
UODuck1879
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
• Mar 4th 2010, 05:49 PM