How do you find the derivative of #root3(x^-5)#?

Answer 1

#-5/3 root(3){x^-8}#

Note that the given function is of the form #x^n# with #n=-5/3# Using #d/{dx}(x^n)=n x^{n-1}# immediately leads to the answer.

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Answer 2

Emma Aldridge

To find the derivative of √3(x^-5), you would use the chain rule of differentiation. First, rewrite the function as (x^-5)^(1/√3). Then, differentiate using the chain rule, which states that the derivative of f(g(x)) is f'(g(x)) * g'(x). The derivative of (x^-5)^(1/√3) is (1/√3)(x^-5)^(1/√3 - 1) * -5x^(-5 - 1). Simplify this expression to get the derivative.

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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.