Derivative of Exponential equation

[Euler]

I am stuck on this problem. I'm trying to find the derivative of 3^x. The answer in the back of the book is ~9.89. I've never done derivatives with the x as an exponent, and when I try to bring it down as I would a normal derivative, I get just plain 9.

 

[Matt]

3^x = e^{x * ln(3)}

and the chain rule.

 

[Euler]

Thanks. I found it buried in my Calculus for Dummies book soon after I made this post. I was wondering if you know how the formula is derived?

 

[Matt]

I found it buried in my Calculus for Dummies book...

What did you find buried in your calculus book?

I was wondering if you know how the formula is derived?

How which formula is derived? Did you read my post?

 

[Euler]

What i found buried in the calc book was the ln formula. I had made a calculation error and thought I had found the wrong thing!

Yes, I read your post. I wanted to know if you knew how the actual formula was derived. I know the formula. I just am interested to know its derivation.

 

[tkhunny]

It can be derived quite easily by observing Matt's suggestion already posted. Otherwise, have you met "logarithmic differentiation"?

 

[Euler]

No. I'll just have to wait for it then won't I? We'll get to it one day. I'm ahead of the calculus class. Didn't want to do the guess-and-check method that the book is trying to have us do, so I just did normal derivatives.