# How do you find the derivative of #g(x)=root4(x)#?

The answer is

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To find the derivative of ( g(x) = \sqrt[4]{x} ), you can use the power rule for differentiation, which states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). Applying this rule to ( g(x) = \sqrt[4]{x} ), we have:

[ g'(x) = \frac{1}{4}x^{\frac{1}{4}-1} ]

Simplify the exponent:

[ g'(x) = \frac{1}{4}x^{-\frac{3}{4}} ]

So, the derivative of ( g(x) = \sqrt[4]{x} ) is ( g'(x) = \frac{1}{4}x^{-\frac{3}{4}} ).

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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.

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.

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.

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