Find The Derivative of x x

Find the first derivative of y = x x for x > 0 with all the steps presented.

Derivative of x x with Steps

Note that the function y = x x is neither a power function of the form x k nor an exponential function of the form b x and the known formulas of Differentiation of these two functions cannot be used. We need to find another method to find the first derivative of the given function.
Function y = x^x
Take the natural log (ln) of both sides of the above
ln Equation
Use properties of logarithmic functions   ln Ab = b ln A   to the right side of the above equation and obtain
ln(y) = x ln(x)
Differentiate both sides of the above with respect to x , using the chain rule on the left side and the product rule on the right.
Differentiation Simplify the right side Differentiation
Multiply both sides by y and simplify
Derivative of y
Substitute y by x x to obtain the final answer
Final Derivative of y


Find the first derivative of

Answer to the Above Exercise:

More References and Links

differentiation and derivatives