Use the Chain Rule to find dw/dt. (Enter your answer only in terms of t.)

w = xey / z, x = t6, y = 9 - t, z = 4 + 4t ... ?

We substitute the values of x, y and z into w to get an equation only in terms of t.

w = x * exp (y) / z

w = t⁶ x exp (9 - t) / (4 + 4t)

Now, in order to differentiate, we must apply the product and quotient rule of differentiation:

dw/dt = 6t⁵ * exp (9 - t) / (4 + 4t) + t⁶ [ - (4 + 4t) exp (9 - t) - 4 (exp (9 - t)) / (4 + 4t) ²]

This can be simplified further to obtain an easier expression.