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How do you find the derivative of #f(x)=root5(x)#?

Answer 1

Scarlett Allison

#f(x)=root5x#

#f(x)=x^(1/5)#

#f'(x)=1/5x^(-4/5)#

#f'(x)=1/[5x^(4/5)]#

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Answer 2

Scarlett Allison

To find the derivative of (f(x) = \sqrt{5x}), you can use the power rule for differentiation.

The power rule states that if you have a function of the form (g(x) = x^n), then its derivative is (g'(x) = nx^{n-1}).

In this case, you can rewrite (f(x)) as (f(x) = 5x^{1/2}). Applying the power rule, the derivative of (f(x)) is:

[f'(x) = \frac{1}{2} \cdot 5x^{1/2 - 1}] [f'(x) = \frac{5}{2}x^{-1/2}] [f'(x) = \frac{5}{2\sqrt{x}}]

So, the derivative of (f(x) = \sqrt{5x}) is (f'(x) = \frac{5}{2\sqrt{x}}).

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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.