Question

1) Calcule a derivada das funções abaixoa) f(x)= (2x2-3x+1)6

Answer 1

Usando a Regra da cadeia:

$f(x)=(2x^2-3x+1)^6\\ \\ u=2x^2-3x+1\\ \\ f(x)=u^6\\ \\ \boxed{\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}}\\ \\ \frac{dy}{du}=6u^5=6(2x^2-3x+1)^5\\ \\ \frac{du}{dx}=4x-3\\ \\ f'(x)=\frac{dy}{dx}=[6(2x^2-3x+1)^5].(4x-3)\\ \\ f'(x)=6 (4 x-3) (2 x^2-3 x+1)^5$