Differentiate the function

Question

g(x) = x2(1 − 8x)

Answer 1

Two ways to do it.

 

First, multiply the RHS out then differentiate using the Sum and Power rules:

     g(x) = x²(1-8x)

     g(x) = x² - 8x³

     g'(x) = d(x²)/dx - d(8x³)/dx

     g'(x) = 2x - 24x²

 

Second way is to apply the Product Rule:

     g(x) = x²(1-8x)
     g'(x) = (1-8x)·d(x²)/dx - x²·d(1-8x)/dx

     g'(x) = (1-8x)·2x - x²·(8)

     g'(x) = 2x - 16x² - 8x²

     g'(x) = 2x - 24x²