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Power rule

The power rule is used to calculate the derivative of a power function



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


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