Question

Considere a função:
y = etan(x)
A derivada dessa função é:

Answer 1

$\boxed{y=e^{\tan{x}}}$

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=\bigg[\dfrac{\mathrm{d}}{\mathrm{d}x}\left(e^{\tan{x}}\right)\bigg]\bigg[\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\tan{x}\right)\bigg]$

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=\left[3^{\tan{x}}\right][\sec^2{x}]$

$\boxed{\dfrac{\mathrm{d}y}{\mathrm{d}x}=3^{\tan{x}}\sec^2{x}}$