Calculus Homework

[Chriscross3234]

How do you find the derivative of a constant raised to the xth power? I'm working on an implicit differentiation of inverse trig fuctions problem where you have to find x' of arctan(6^x). I know you have to use the chain rule here and the first half I can do, but the second half is confusing me.

Thanks

 

[cirthix]

Let's modify the problem:
Find an A so that: 6^x=(e^A)^x=e^Ax
A=ln6 (e^ln6=6)

f(x)=6^x=e^(x*ln6)
f'(x)=ln6*e^xln6 (chain rule and the fact that e^x is it's own derivative)

does that explain it for you?

 

[Chriscross3234]

Aha thanks for the quick response, I understand that fully now. I forgot you had to use natural log for cases like that. Got the problem right too. Thanks again