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How do you find the derivative of #g(x)=1/sqrtx#?

Answer 1

Christopher Allers

see below

#g(x)=1/sqrtx#

#=>d/dxg(x)=d/dx(x)^(-1/2)#

Utilize the formula,

#d/dxx^n=nx^(n-1)#

#=>d/dx(x)^(-1/2)=-1/2x^((-1/2-1))=-1/(2xsqrtx)#

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Answer 2

Christopher Agresta

To find the derivative of ( g(x) = \frac{1}{\sqrt{x}} ), you can use the power rule for differentiation, which states that the derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ). Apply this rule to the given function:

[ g'(x) = \frac{d}{dx} \left( \frac{1}{\sqrt{x}} \right) ]

[ = \frac{d}{dx} \left( x^{-\frac{1}{2}} \right) ]

[ = -\frac{1}{2}x^{-\frac{1}{2} - 1} ]

[ = -\frac{1}{2}x^{-\frac{3}{2}} ]

[ = -\frac{1}{2\sqrt{x^3}} ]

Therefore, the derivative of ( g(x) = \frac{1}{\sqrt{x}} ) is ( g'(x) = -\frac{1}{2\sqrt{x^3}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.