How do you differentiate $y = \frac{e^{x}}{x^{2}}$ $y=e^x/x^2$ ?

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Answer 1 · 2016-11-30T15:38:53

The answer is $= \frac{e^{x} (x - 2)}{x^{3}}$ $=(e^x(x-2))/x^3$

We use the derivative of a quotient

$(u/v)'=(u'v-uv')/(v^2)$

$u=e^x$ , $=>$ , $u'=e^x$

$v=x^2$ , $=>$ , $v'=2x$

So, $dy/dx=(e^x*x^2-e^x*2x)/(x^4)$

$=(xe^x(x-2))/(x^4)=(e^x(x-2))/x^3$

How do you differentiate y=e^x/x^2y=exx2y=e^x/x^2?