Question

qual a derivada de f (x)= e^x/ 1 + x​

Answer 1

Oie, Td Bom?!

$f(x) = \frac{e {}^{x} }{1 + x}$

$f'(x) = \frac{d}{dx} ( \frac{e {}^{x} }{1 + x} )$

$f'(x) = \frac{ \frac{d}{dx} (e {}^{x}) \: . \: (1 + x) - e {}^{x} \: . \: \frac{d}{dx} (1 + x)}{(1 + x) {}^{2} }$

$f'(x) = \frac{e {}^{x} \: . \: (1 + x) - e {}^{x} \: . \: 1 }{(1 + x) {}^{2} }$

$f'(x) = \frac{e {}^{x} + xe {}^{x} - e {}^{x} }{(1 + x) {}^{2} }$

$f'(x) = \frac{xe {}^{x} }{(1 + x) {}^{2} }$

Att. Makaveli1996