Question

What is the derivative of `1/sqrtx`?

Answer 1

Oe law of exponentials states that `a^-n=1/a^n`. Also, another law states that `a^(m/n)=root(n)(a^m)`. Finally, we'll need a third one: `(a^n)^m=a^(n*m)`

Thus, we can rewrite this function following both laws. Then, we derivate it.

First law applied:

`(sqrtx)^-1`

Second law:

`(x^(1/2))^-1`

Third law mentioned:

`x^(-1/2)`

Now, deriving `f(x)=x^(-1/2)`

`(dy)/(dx)=(-1/2)x^(-3/2)=-1/(2x^(3/2))`

Or, if you prefer the root: `-1/(2sqrt(x^3))`