Thread: Partial derivative chain rule

Let z = g(x, y) and suppose that x(t) = t^2 + 3t + 2 and y(t) = e^t + sin(3t)

Find (dz/dt)|t=0

if (dg/dx)|(1,2) = 6
(dg/dy)|(1,2) = -2
(dg/dx)|(2,1) = -3
(dg/dy)|(2,1) = 8
(dg/dx)|(0,0) = 0
(dg/dy)|(0,0) = -4

Thank You.

Originally Posted by DavidWagner

Let z = g(x, y) and suppose that x(t) = t^2 + 3t + 2 and y(t) = e^t + sin(3t)

Find (dz/dt)|t=0

if (dg/dx)|(1,2) = 6
(dg/dy)|(1,2) = -2
(dg/dx)|(2,1) = -3
(dg/dy)|(2,1) = 8
(dg/dx)|(0,0) = 0
(dg/dy)|(0,0) = -4

Thank You.

By the Chain rule we get



Now we need to do some calculations

and

so
and


so Finally we get