## anonymous one year ago What rules of derivatives and method do you use to work out the derivative to f[x]=2^x ?

1. anonymous

I just realized in a whole chapter on derivatives, they never covered this one

2. UsukiDoll

there's a rule $\frac{d}{dx} a^x = a^x \cdot \ln a$

3. UsukiDoll

The derivative of an exponential function with base a is equal to the natural logarithm of that base times the exponential function.

4. UsukiDoll

so just a = 2 and plug it into that exponential rule

5. anonymous

thanks usuki.. is something to do with the change of base formula?

6. UsukiDoll

?! it's just another derivative rule. In Calculus II THERE ARE LOTS OF THEM!

7. anonymous

lol, oh so there are more coming than just the good ol chain rule.

8. UsukiDoll

oh yeah .

9. ganeshie8

$\large f(x)=2^x = e^{\ln 2^x} = e^{x*\ln 2}$ you may use the good ol chain rule now

10. anonymous

:) where there is a will

11. UsukiDoll

ewwwwww I prefer the earlier version.. much faster.

12. ganeshie8

both are same

13. anonymous

you got my vote, but that is definitely an enlightening idea for someone at my stage of learning

14. UsukiDoll

$\frac{d}{dx} a^x = a^x \cdot \ln a$ ftw kthxbai!

15. ganeshie8

are you suggesting to memorize a new formula

16. UsukiDoll

what's wrong with that? it's easier and straight to the point

17. ganeshie8

there is nothing wrong with that its only that i felt the op wants to work it out using chain rule

18. anonymous

I fully appreciate both perspectives here. exploring how we come up with the rule helps me as this road twists and turns.

19. anonymous

and of course, just having the rule is the kind of practical approach that gets cuts through this experience with no bs, gotta love that.