Question

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

Answer 1

`-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)`