brainmatter
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#1
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why does y= a^x differentiate to a^xlna

i dont get the logic behind it
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Hody421
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ln(a) is a constant

Differentiate 9x you get 9
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pleasedtobeatyou
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(Original post by brainmatter)
why does y= a^x differentiate to a^xlna

i dont get the logic behind it
Take logs of both sides:

ln(y) = x \ ln(a)

\dfrac{1}{y} \dfrac{dy}{dx} = ln(a)

\dfrac{dy}{dx} = y \ ln(a)

\dfrac{dy}{dx} = a^x \ ln(a)
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rakib567
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brainmatter
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(Original post by pleasedtobeatyou)
Take logs of both sides:

ln(y) = x \ ln(a)

\dfrac{1}{y} \dfrac{dy}{dx} = ln(a)

\dfrac{dy}{dx} = y \ ln(a)

\dfrac{dy}{dx} = a^x \ ln(a)

how is this taking logs of both sides, wouldn't it be a on RHS if logs of both sides was taken?
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pleasedtobeatyou
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(Original post by brainmatter)
how is this taking logs of both sides, wouldn't it be a on RHS if logs of both sides was taken?
Apply the log function to both sides. log(y) = log(x^a)

Bring down the exponent, using the property of logs, on the RHS to get log(y) = alog(x)
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Krollo
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You could also write a^x = e^(xlna)

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