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

1 Answer
Apr 25, 2016

Answer:

#-3/2x^(-5/2)#

Explanation:

The most important thing here is not calculus but algebra. In particular, the properties of exponents.

Note that #sqrt(1/x^3)# is equivalent to #sqrt(x^(-3))# (because #1/a# is equal to #a^(-1)#). Using the property #root(a)(x^b)=x^(b/a)#, #root(2)(x^(-3))=x^(-3/2)#. Our problem now is simply finding the derivative of #x^(-3/2)#, which is done easily using the power rule:
#d/dxx^(-3/2)=-3/2*x^(-3/2-1)=-3/2x^(-5/2)#