Wondermath
What's the derivative of the following? (I will draw it)



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Wondermath
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dw:1335940380736:dw

Wondermath
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is it e^(x/2)ln2

nustian
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1/2e^1/2x

bmp
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I think it's only \(\LARGE \frac{e^{x/2}}{2} \) Isn't it? It can be rewritten as e^(x/2)

Wondermath
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can u tell me how you got it?

bmp
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Rewrite it as \[ e^\frac{x}{2} \]Then the derivative of e^u is e^u u', right? So we have derivative of that = e^(x/2) * d(x/2) = 1/2 :)

nbouscal
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\[\huge
(\sqrt{e})^x=(e^{1/2})^x=e^{x/2}
\]
Apply chain rule to get
\[\huge
e^{x/2} \over\huge 2
\]

kropot72
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\[(\sqrt{e})^{x}=(e ^{1/2})^{x}=e ^{x/2}\]

nustian
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dw:1335940696779:dw

thomas5267
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The winner of the LaTeX speed competition is...@bmp ! Congratulations!

Wondermath
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thanks guys :)