# What does (1/2)x^(-1/2) equal?

#### coolbeans33

##### New member
I know that the derivative of the sqrt x = .5x^-1/2

I think that x^-1 equals 1/x right?

so what does .5x^-1/2 equal? Im kind of confused!

is it 1/4x?

#### Chris L T521

##### Well-known member
Staff member
Re: what does 1/2x^-1/2 equal?

I know that the derivative of the sqrt x = .5x^-1/2

I think that x^-1 equals 1/x right?

so what does .5x^-1/2 equal? Im kind of confused!

is it 1/4x?
Since there are no parenthesis, then $.5x^{-1/2} = .5\cdot x^{-1/2}= \dfrac{.5}{x^{1/2}} = \dfrac{1}{2x^{1/2}}$.

I hope this clarifies things!

#### Prove It

##### Well-known member
MHB Math Helper
Re: what does 1/2x^-1/2 equal?

Since there are no parenthesis, then $.5x^{-1/2} = .5\cdot x^{-1/2}= \dfrac{.5}{x^{1/2}} = \dfrac{1}{2x^{1/2}}$.

I hope this clarifies things!
$$\displaystyle = \frac{1}{2\sqrt{x}}$$