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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just realized in a whole chapter on derivatives, they never covered this one

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1there's a rule \[\frac{d}{dx} a^x = a^x \cdot \ln a \]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1The derivative of an exponential function with base a is equal to the natural logarithm of that base times the exponential function.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1so just a = 2 and plug it into that exponential rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks usuki.. is something to do with the change of base formula?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1?! it's just another derivative rule. In Calculus II THERE ARE LOTS OF THEM!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol, oh so there are more coming than just the good ol chain rule.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\large f(x)=2^x = e^{\ln 2^x} = e^{x*\ln 2}\] you may use the good ol chain rule now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:) where there is a will

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1ewwwwww I prefer the earlier version.. much faster.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you got my vote, but that is definitely an enlightening idea for someone at my stage of learning

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{d}{dx} a^x = a^x \cdot \ln a \] ftw kthxbai!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1are you suggesting to memorize a new formula

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1what's wrong with that? it's easier and straight to the point

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1there is nothing wrong with that its only that i felt the op wants to work it out using chain rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I fully appreciate both perspectives here. exploring how we come up with the rule helps me as this road twists and turns.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and of course, just having the rule is the kind of practical approach that gets cuts through this experience with no bs, gotta love that.
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