Derivative of Exponential and Logarithmic Function Concept Question

[jacksonpeeble]

Homework Statement

y=9^-x

Homework Equations

The Attempt at a Solution

dy/dx=-9^-xln9

We are provided with the answers. I do not understand the concept behind how to get from the question to the solution. What rule(s) are applied? If somebody could solve this single question, or a similar one, in a step-by-step method, I would greatly appreciate it.

 

[Mark44]

Do you know how to find d/dx(e^u)? If so, you can rewrite 9^-x as (e^{ln 9})^-x and use that derivative formula on it. You'll also want to use the fact that (a^r)^s = a^rs.

Welcome back! Haven't heard from you for a while.

 

[jacksonpeeble]

Thank you, that is very helpful. It makes sense, but it really seems kind of roundabout... ah, well. Calculus...

Thank you! Lately I've either been able to do my homework (or at least I've suffered in silence), although I'm taking AP Physics this year and I've posted some on that forum, and I occasionally try to contribute on the Pre-Calc boards when possible.