Finding the Derivative of Trigonometric Functions with Exponents?

[Taryn]

hey I have this question and have looked it up in the textbook and web sites but can't seem to find what to do!
Any assistance would be appreciated thanks!

Find the first derivative w.r.t the relevant variable
5^(sin(theta))

I am guessin the relevant variable is theta but I don't even no where to go from that!

 

[Tomsk]

First thing is to write it as

y = 5^sin(theta)

Then take logs of both sides and differentiate implicitly to get dy/dtheta.

 

[Taryn]

haha, that's helpful! I don't know y I didnt think of that, thanks so much! Appreciate it!

 

[NateTG]

Or, if you're feeling less industrious, the chain rule also works.

 

[HallsofIvy]

But to use the chain rule, you have to know that the derivative of 5^x is (ln(5))5^x.