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

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SUMMARY

The expression (1/2)x^(-1/2) simplifies to 1/(2√x). This is derived from the understanding that x^(-1) equals 1/x, and thus 0.5x^(-1/2) can be rewritten as 0.5 divided by x^(1/2). The final result confirms that the correct interpretation of the expression is 1/(2√x), clarifying any confusion regarding its simplification.

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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?
 
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Re: what does 1/2x^-1/2 equal?

coolbeans33 said:
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!
 
Re: what does 1/2x^-1/2 equal?

Chris L T521 said:
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}} :)
 

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