 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/2/a/solution

For positive

a

, write

a^{- x} = exp (- x ln a)

. Differentiating by the chain rule gives

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

The natural logarithm of the constant base supplies the factor; it must not be omitted when

a \neq = e

 New to topics? Read the docs here!