- #1

QuickLoris

- 12

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The derivative of [itex]a^{x}[/itex] is [itex]a^{x}[/itex]lna.

The explanation that Stewart 5e gives is:

[itex]\frac{d}{dx}[/itex][itex]a^{x}[/itex] = [itex]\frac{d}{dx}[/itex][itex]e^{(lna)x}[/itex]

= [itex]e^{(lna)x}[/itex][itex]\frac{d}{dx}[/itex](lna)x

=[itex]e^{(lna)x}[/itex][itex]\cdot[/itex]lna

=[itex]a^{x}[/itex]lna

My question is: Why do we use the natural log instead of a log of any other base?