Question

se f(x) e g(x) são funções tais que g(0) = 1, f'(1) = 2, g'(0) = 1, então a derivada da função f( x + g(x) ) em x = 0 é igual a :

R: 4

Answer 1

Olá!!

Seja $\mathbf{h(x) = f(x + g(x))}$. Determinemos $\mathbf{h'(x)}$.

$\\ \displaystyle \mathsf{h(x) = f(x + g(x))} \\\\ \mathsf{h'(x) = f'(x + g(x)) \cdot (x + g(x))'} \\\\ \mathsf{h'(x) = f'(x + g(x)) \cdot (1 + g'(x))} \\\\ \mathsf{h'(0) = f'(0 + g(0)) \cdot (1 + g'(0))} \\\\ \mathsf{h'(0) = f'(0 + 1) \cdot (1 + 1)} \\\\ \mathsf{h'(0) = f'(1) \cdot 2} \\\\ \mathsf{h'(0) = 2 \cdot 2} \\\\ \boxed{\mathsf{h'(0) = 4}}$