Find the first derivative of y = x x for x > 0 with all the steps presented.
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.
Given
Take the natural log (ln) of both sides of the above
Use properties of logarithmic functions ln Ab = b ln A to the right side of the above equation and obtain
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.
Simplify the right side
Multiply both sides by y and simplify
Substitute y by x x to obtain the final answer
Find the first derivative of
Answer to the Above Exercise:
differentiation and derivatives
