Question

A derivada de f(x) = [(x+1)/(x+2)]*(3x^2+6x)?

Answer 1

$\mathrm{f(x)=\bigg(\dfrac{x+1}{x+2}\bigg)(3x^2+6x)\ \to\ f(x)=3x\bigg(\dfrac{x+1}{x+2}\bigg)(x+2)}\\\\ \mathrm{f(x)=3x(x+1)\ \to\ f(x)=3x^2+3x}\\\\ \mathrm{f'(x)=3\frac{d}{dx}(x^2)+3\frac{d}{dx}(x)\ \to\ f'(x)=3.2x+3.1}\\\\ \boxed{\mathbf{f'(x)=6x+3}}$