Power rule
The power rule is used to calculate the derivative of a power function
Explanation
The function f (x) = xx can not easily be differentiated, because both the base and the exponent are variable. By first taking the logarithm, we eliminate the exponent
what we convert to
Now we implicitly differentiate both sides to x
The left side can be calculated using the chain rule
The derivative of the logarithm and the product rule gives
Multiplying by y gives
Set again y = xx, then the solution is