Question

Suponha que f seja derivável em R. Sejam F(x)=f(e^x) e G(x)=e^f(x). Calcule F’(x) e G’(x).

Answer 1

$\mathsf{F(x)={e}^{x}}$

$\large\boxed{\boxed{\mathsf{F'(x)={e}^{x}}}}$

$\mathsf{G(x)= { {e}^{x} }^{ {e}^{x} } = {e}^{x {e}^{x} } }$

$\mathsf{G'(x)={e}^{x{e}^{x}}.({e}^{x}+x{e}^{x})} \\ \mathsf{G'(x)={e}^{x{e}^{x}}.{e}^{x}(1+x) }$