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

Answer 1

Luke Alvarez

The answer is #=1/(4root(4)(x^3))#

We use

#(x^n)'=nx^(n-1)#

#g(x)=root(4)x=x^(1/4)#

#g'(x)=1/4*x^(1/4-1)#

#=1/4x^(-3/4)=1/(4root(4)(x^3))#

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Answer 2

Scarlett Allison

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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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.