Write a rule for f(x) = a^x where a is a constant

**ffezz** · March 17th 2008, 05:22 PM

Hi
I need to write a rule for the derivative of $f(x) = a^x$ where a is a constant. I was thinking of $xa^x-1$ but my teacher said that is not what he is looking for. By the way i cant seem to get it to put the entire exponent up which is (x-1).
Any ideas?

**topher0805** · March 17th 2008, 05:38 PM

The derivative of $a^x$ will always be $a^x\cdot ln a$

The way to get the entire exponent is to put it in curly brackets: {x-1}

**o_O** · March 17th 2008, 05:55 PM

Seems like your teacher is asking you to prove it?

Note that: $a^{x} = e^{ln\left(a^{x}\right)} = e^{xlna}$

If you know that $\frac{d}{dx}e^{x} = e^{x}$ and know how to use the chain rule, then you should be able to find the derivative of $a^{x}$

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