Posted by **Anonymous** on Wednesday, January 28, 2009 at 5:30pm.

How would one take the derivative of "f(x)^[g(x)]? Is there a formula I can follow to differentiate functions like that?

- Math - Derivatives -
**Reiny**, Wednesday, January 28, 2009 at 7:03pm
you will have to take the natural log of both sides.

I will illustrate with an example

e.g.

y = (x^2+1)^(2x+3)

ln y = ln ((x^2+1)^(2x+3))

ln y = (2x+3)(ln(x^2+1)

now differentiate, using the product rule on the right side.

(dy/dx)/y = (2x+3)(2x/(x^2+1)) + 2ln(x^2+1)

dy/dx = y((2x+3)(2x/(x^2+1)) + 2ln(x^2+1))

you could then replace y with its original value and simplify, but that would be a general method.

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