 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/8/a/solution

For

a > 0

, write

a^{x} = e^{x l n a}

and apply the chain rule:

\frac{d}{d x} a^{x} = (ln a) a^{x} .

This also covers

a = 1

, for which both sides are zero.

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