# How do you find the derivative of #root4(lnx)#?

We use the chain rule here.

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To find the derivative of (\sqrt[4]{\ln(x)}), you can use the chain rule. The derivative of (f(g(x))) with respect to (x) is (f'(g(x)) \cdot g'(x)).

Let (f(u) = \sqrt[4]{u}) and (g(x) = \ln(x)).

Then (f'(u) = \frac{1}{4} u^{-\frac{3}{4}}) and (g'(x) = \frac{1}{x}).

Now, substitute into the chain rule formula:

(f'(g(x)) \cdot g'(x) = \frac{1}{4} (\ln(x))^{-\frac{3}{4}} \cdot \frac{1}{x}).

So, the derivative of (\sqrt[4]{\ln(x)}) is (\frac{1}{4x(\ln(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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