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

[coolbeans33]

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? I am kind of confused!

is it 1/4x?

 

[Chris L T521]

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? I am 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]

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}} :)