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

Applying the quotient rule:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of (\frac{\ln x}{x^{1/3}}), you can use the quotient rule. The quotient rule states that if you have a function of the form ( \frac{u}{v} ), then the derivative is given by ( \frac{u'v - uv'}{v^2} ), where ( u' ) and ( v' ) represent the derivatives of ( u ) and ( v ) respectively.

Let ( u = \ln x ) and ( v = x^{1/3} ). Then ( u' = \frac{1}{x} ) and ( v' = \frac{1}{3}x^{-2/3} ).

Applying the quotient rule:

[ \frac{d}{dx} \left( \frac{\ln x}{x^{1/3}} \right) = \frac{(1/x)(x^{1/3}) - (\ln x)((1/3)x^{-2/3})}{(x^{1/3})^2} ]

Simplify this expression to get the derivative of the function.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7