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Differentiating to the power of x.

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Differentiating to the power of x.

Neo1

Hello, I just dont know how to differentiate something to the power of x..

For example

y = 10^x

Thanks!

Reply 1

generalebriety

Well, 10^x = e^(x ln 10) = (e^x)^ln 10, and you know how to differentiate that.

Reply 2

EvenStevens

Take logs

y = 10^{x}

ln(y) = \ln(10^{x})

ln(y) = x \ln(10)

Then differentiate (using the product rule for the x ln10)

\frac{1}{y}\frac{dy}{dx} = \ln(10)

\frac{dy}{dx} = y \ln(10)

Then replace y back in

\frac{dy}{dx} = 10^{x} \ln(10)

Reply 3

dreadnaut

what he said ^

\frac{d}{dx} A^x -> (A^x)(lnA)

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Differentiating to the power of x.

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