Question

Calcule a primeira derivada da seguinte função

f(x) = x.tg(4x)


Nenhuma das alternativas


tg(4x) + 4x.sec2(4x)


cos(4x) + 4x.sec2(4x)


tg(4x) + 4x.sec2(x)


tg(x) + 4x.sec2(4x)

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Regra~da~cadeia}\\\sf [f(g(x))]'=f'[g(x)]\cdot g'(x)\\\underline{\rm Derivada~do~produto}\\\sf [f(x)\cdot g(x)]'=f'(x)\cdot g(x)+f(x)\cdot g'(x)\\\underline{\rm Derivada~da~func_{\!\!,}\tilde ao~tangente}\\\sf \dfrac{d}{dx}[tg(u)]=sec^2(u)\cdot\dfrac{du}{dx}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf f(x)=x\cdot tg(4x)\\\sf f'(x)=1\cdot tg(4x)+x\cdot sec^2(4x)\cdot 4\\\sf f'(x)=tg(4x)+4x\cdot sec^2(4x)\end{array}}$