Differentiate a^x

1. Set y=a^x

2. Take the natural log of both sides: ln(y)=ln(a^x)

3. Using the log rules, simplify: ln(y)=xln(a)

4. Differentiate both sides with respect to x: 1/y dy/dx=lna+0

5. Rearrange: dy/dx=yln(a)

6. Using the definition of 'y' set in step 1: dy/dx=a^(x)ln(a)

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