# What is the derivative of #(1-x^2)/(x^3)#?

##### 1 Answer

May 14, 2016

#### Explanation:

Split up the fraction and rewrite it with negative exponents:

#(1-x^2)/x^3=1/x^3-x^2/x^3=x^-3-x^-1#

Now, differentiate

#d/dx(x^-3-x^-1)=(-3)x^(-3-1)-(-1)x^(-1-1)#

#=-3x^-4+x^-2#

This is a valid final answer, but we can also write it without negative exponents by multiplying it by

#(x^4(-3x^-4+x^-2))/x^4=(-3+x^2)/x^4=(x^2-3)/x^4#