Question

encontrar a derivada de f (x )= e^x/x^2​

Answer 1

Oie, Td Bom?!

$f(x) = \frac{e {}^{x} }{x {}^{2} }$

$f'(x) = \frac{d}{dx} ( \frac{e {}^{x} }{x {}^{2} } )$

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

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

$f'(x) = \frac{x \: . \: (e {}^{x}x - e {}^{x} \: . \: 2) }{x {}^{4} }$

$f'(x) = \frac{xe {}^{x} - 2e {}^{x} }{x {}^{3} }$

Att. Makaveli1996