# What is the derivative of #x^sin(x)#?

Take the natural logarithm of both sides.

Use laws of logarithms to simplify.

Use the product rule and implicit differentiation to differentiate.

Hopefully this helps!

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

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

Use logarithmic differentiation.

Use implicit differentiation on the left side:

Use the product rule on the right sides:

Substituting into the product rule:

Put the equation back together:

Multiply both sides by y:

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

The derivative of ( x^{\sin(x)} ) with respect to ( x ) is given by ( x^{\sin(x)}(\ln(x)\cos(x)+\frac{\sin(x)}{x}) ).

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