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

Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
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.
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)