What is the derivative of 1/sqrtx?

1 Answer
Guilherme N.
Jun 2, 2015

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))

Related questions
See all questions in Quotient Rule
Impact of this question
1657 views around the world
You can reuse this answer
Creative Commons License