# How do you find the derivative of #y= ((e^x)/(x^2)) #?

##### 1 Answer

Jan 13, 2016

#### Explanation:

You can use the quotient rule to find the derivative.

If

#f'(x) = (h(x) g'(x) - g(x) h'(x) ) / (h^2(x)) #

In your case,

#g(x) = e^x# and#h(x) = x^2# .

The derivatives of

#g'(x) = e^x# and#h'(x) = 2x# .

Thus, according to the formula, you derivative is:

#f'(x) = (x^2 * e^x - e^x * 2x ) / (x^2)^2 = (x e^x (x - 2)) / (x^4)#

... cancel

#= (cancel(color(blue)(x)) e^x (x - 2)) / (x^3 * cancel(color(blue)(x))) = (e^x (x-2) ) / (x^3) #