Question

Derivada de f(x)=(x^5-7)(2x^3+x^2+x-5)

Answer 1

Regra do produto:

$f(x)=(x^5-7)(2x^3+x^2+x-5)\\\\f'(x)=(x^5-7)'(2x^3+x^2+x-5)+(x^5-7)(2x^3+x^2+x-5)'\\\\f'(x)=(5x^4)(2x^3+x^2+x-5)+(x^5-7)(6x^2+2x+1)\\\\f'(x)=10x^7+5x^6+5x^5-25x^4+6x^7+2x^6+x^5-42x^2-14x-7\\\\\boxed{f'(x)=16x^7+7x^6+6x^5-25x^4-42x^2-14x-7}$