If f(x) = (x3 - 4)7, then what is f '(x)?

Question

If f(x) = (x3 − 4)7, then what is f '(x)?

Answer 1

If u is a function of x and n is a real number, then by the Chain Rule, d/dx(uⁿ) = nu^n-1(du/dx)

 

So, if f(x) = (x³-4)⁷, then f'(x) = 7(x³-4)⁶(3x²)

 

                                               = 21x²(x³-4)⁶