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

Question

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

anonymous · Answer

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

usukidoll · Answer

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

usukidoll · Answer

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

usukidoll · Answer

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

anonymous · Answer

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

usukidoll · Answer

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

anonymous · Answer

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

usukidoll · Answer

oh yeah .

ganeshie8 · Answer

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

anonymous · Answer

:) where there is a will

usukidoll · Answer

ewwwwww I prefer the earlier version.. much faster.

ganeshie8 · Answer

both are same

anonymous · Answer

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

usukidoll · Answer

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

ganeshie8 · Answer

are you suggesting to memorize a new formula

usukidoll · Answer

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

ganeshie8 · Answer

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

anonymous · Answer

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

anonymous · Answer

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.