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#
