# How do you find the derivative of # ln[x]/x^(1/3)#?

Use quotient rule:

Simplify:

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To find the derivative of ln[x]/x^(1/3), you can use the quotient rule. The derivative of the quotient f(x)/g(x) is (f'(x)g(x) - f(x)g'(x)) / [g(x)]^2. Applying this rule to ln[x]/x^(1/3), where f(x) = ln[x] and g(x) = x^(1/3), and taking derivatives of f(x) and g(x) separately, you get:

f'(x) = 1/x and g'(x) = (1/3)x^(-2/3).

Substituting these into the quotient rule formula, you get:

[1/x * x^(1/3) - ln[x] * (1/3)x^(-2/3)] / [x^(1/3)]^2.

Simplify this expression to get the final derivative.

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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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