How Do You Evaluate dw/dt at t=0 Using the Chain Rule Results?

[Whatupdoc]

Suppose w = x/y + y/z

x = exp(t), y=2+sin(5t), and z= 2+cos(7t)

A.) Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite exp(t) as x. I got this one right, the answer is 1/y*exp(t) +(- x/y^2+1/z)*(5*cos(5t)) + (-y/z^2)*(-7sin(7t)).

i need help on B.

B.) Use part A to evaluate dw/dt when t=0
i just plugged in zeros for t, but i get an answer with the variables y and z, which i shouldn't have. what am i suppose to do for this question?

 

[quasar987]

Suppose w = x/y + y/z

x = exp(t), y=2+sin(5t), and z= 2+cos(7t)

A.) Use the chain rule to find dw/dt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite exp(t) as x. I got this one right, the answer is 1/y*exp(t) +(- x/y^2+1/z)*(5*cos(5t)) + (-y/z^2)*(-7sin(7t)).

i need help on B.

B.) Use part A to evaluate dw/dt when t=0
i just plugged in zeros for t, but i get an answer with the variables y and z, which i shouldn't have. what am i suppose to do for this question?

Well x, y and z are functions of t aren't they? So when you set t=0, you've GOT to write x, y and z in terms of t, and then set t=0 in the resulting equation.

 

[Whatupdoc]

yup, thanks a lot