Question

Find the derivative of the function by using the Product Rule. Simplify your answer. f(x)=(x⁴ +1)(x⁴ −1)

Answer 1

Hi,

Explanation:

It is not very cleaver to use the Product Rule!

`f(x)=(x^4+1)(x^4-1)=x^8-1\\f'(x)=8x^7\\but:\\f(x)=(x^4+1)(x^4-1)\\f'(x)=4x^3(x^4-1)+(x^4+1)*4x^3=4x^7-4x^3+4x^7+4x^3=8x^7\\`