Differentiate both sides of the equation.

The derivative of with respect to is .

Use the properties of logarithms to simplify the differentiation.

Rewrite as .

Expand by moving outside the logarithm.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Exponential Rule which states that is where =.

Replace all occurrences of with .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

Move to the left of .

The derivative of with respect to is .

Combine fractions.

Combine and .

Combine and .

Combine and .

Simplify the numerator.

Multiply .

Reorder and .

Simplify by moving inside the logarithm.

Reorder factors in .

Reform the equation by setting the left side equal to the right side.

Replace with .

Find dy/dx y=x^( natural log of x)