This is easy but I am getting something mixed up

Question

All edges of a cube are expanding at a rate of 7 centimeters per second.

(a)How fast is the surface area changing when each edge is 9 centimeters? 

(b)How fast is the surface area changing when each edge is 12 centimeters? 

Answer 1

You are given ^dx/_dt = 7 cm/s (where x is the length of the edge of the cube)

You have been asked to find ^dS/_dt (where S is the surface area of the cube)

You need an expression for ^dS/_dx so that you can use the chain rule: ^dS/_dt = ^dS/_dx x ^dx/_dt

What is the formula for surface area of a cube? S = 6x²

Differentiate: ^dS/_dx = 12x

Now: ^dS/_dt = (12x)(7) = 84x cm²/s

All you need to do now is to plug in x = 9 and x = 12