Question

How do you find the derivative of `sqrt(1/x^3)`?

Answer 1

i think the simplest thing is to rewrite it so that we can use the power rule.

Explanation:

`sqrt(1/x^3) = 1/sqrt(x^3) = 1/x^(3/2) = x^(-3/2)`

So the derivative is

`-3/2x^((-3/2-1)) = -3/2x^(-5/2) = -3/(2sqrt(x^5)) = -3/(2x^2sqrtx)`

Answer 2

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

Explanation:

Start by rewriting the function as.

`y=sqrt(1/(x^3))=(1/x^3)^(1/2)=1/(x^(3/2))=x^(-3/2)`

now differentiate using the `color(blue)"power rule"`

`dy/dx=-3/2x^(-5/2)=-3/(2x^(5/2))`