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

##### 1 Answer

May 21, 2016

#### Explanation:

The first step here is to multiply out the brackets.

#rArr1/2(x^2-x^-2)=1/2x^2-1/2x^-2# Now both terms can be differentiated using the

#color(blue)" power rule"#

#d/dx(ax^n)=nax^(n-1)#

#rArrdy/dx=2xx1/2x^(2-1)-(-2)xx1/2x^(-2-1)# which simplifies to.

#dy/dx=x+x^-3=x+1/x^3#