Question

Consider the following.

w = xy² + x²z + yz², x = t², y = 8t, z = 8

Find dw/dt using the appropriate Chain Rule.
dw/dt=___

Answer 1

To find dw/dt using the Chain Rule, substitute the given values for x, y, and z into the equation for w. Then, find the derivative of w with respect to t.

Step-by-step explanation:

To find dw/dt using the Chain Rule, we first substitute the given values for x, y, and z into the equation for w. This gives us:

w = (t^2)(8t^2)^2 + (t^2)^2(8) + (8t^2)^2
w = 64t^4 + t^4(8) + 64t^4
w = 64t^4 + 8t^4 + 64t^4
w = 136t^4

Next, we find the derivative of w with respect to t. The derivative of 136t^4 with respect to t is:

dw/dt = 4(136t^3)
dw/dt = 544t^3