Question

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

Answer 1

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.