# Calc2.2

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Find the derivative of $f(x)\,$ with respect to $x\,$: $f(x)=g(x)^{{h(x)}}\,$

This is a general form of the previous problem. The same process will be followed and when we are finished we will have a formula which can be used to differentiate any function which involves a function of $x\,$ in the base and another in the exponent.

$f=g^{h}\,$

As before, take the natural log of both sides to change the function into a form of which we can take the derivative.

$\ln f=h\ln g\,$

${\frac {1}{f}}f'=h'\ln g+{\frac {h}{g}}g'\,$

$f'=f(h'\ln g+{\frac {h}{g}}g')\,$

$f'=g^{h}(h'\ln g+{\frac {h}{g}}g')\,$