Question

Qual a derivada de $( 5x^{3} - 2x^{2})^{20}$ ?

Answer 1

Utilize a chamada Regra da cadeia:

$f(x)=(5x^3-2x^2)^{20}\\ \\ u=5x^3-2x^2\\ \\ f(x)=u^{20}\\ \\ f'(x)=\frac{dy}{du}.\frac{du}{dx}\\ \\ f'(x)=20u^{19}.(15x^2-4x)\\ \\ \boxed{f'(x)=20(5x^3-2x)^{19}(15x^2-4x)}$