anonymous
  • anonymous
What rules of derivatives and method do you use to work out the derivative to f[x]=2^x ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I just realized in a whole chapter on derivatives, they never covered this one
UsukiDoll
  • UsukiDoll
there's a rule \[\frac{d}{dx} a^x = a^x \cdot \ln a \]
UsukiDoll
  • UsukiDoll
The derivative of an exponential function with base a is equal to the natural logarithm of that base times the exponential function.

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UsukiDoll
  • UsukiDoll
so just a = 2 and plug it into that exponential rule
anonymous
  • anonymous
thanks usuki.. is something to do with the change of base formula?
UsukiDoll
  • UsukiDoll
?! it's just another derivative rule. In Calculus II THERE ARE LOTS OF THEM!
anonymous
  • anonymous
lol, oh so there are more coming than just the good ol chain rule.
UsukiDoll
  • UsukiDoll
oh yeah .
ganeshie8
  • ganeshie8
\[\large f(x)=2^x = e^{\ln 2^x} = e^{x*\ln 2}\] you may use the good ol chain rule now
anonymous
  • anonymous
:) where there is a will
UsukiDoll
  • UsukiDoll
ewwwwww I prefer the earlier version.. much faster.
ganeshie8
  • ganeshie8
both are same
anonymous
  • anonymous
you got my vote, but that is definitely an enlightening idea for someone at my stage of learning
UsukiDoll
  • UsukiDoll
\[\frac{d}{dx} a^x = a^x \cdot \ln a \] ftw kthxbai!
ganeshie8
  • ganeshie8
are you suggesting to memorize a new formula
UsukiDoll
  • UsukiDoll
what's wrong with that? it's easier and straight to the point
ganeshie8
  • ganeshie8
there is nothing wrong with that its only that i felt the op wants to work it out using chain rule
anonymous
  • anonymous
I fully appreciate both perspectives here. exploring how we come up with the rule helps me as this road twists and turns.
anonymous
  • 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.

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