Question

Differentiating Functions of Other Bases In Exercise, find the derivative of the function.

Answer 1

Answer:

$y' = -\frac{1}{2.3x}$

Step-by-step explanation:

The derivative of $a*x^{n}$ is $a*n*x^{n-1}$. The derivative of $3x^{-1}$ is $-3x^{-2}$, for example.

Derivative of the log function:

$y = \log_{a}{f(x)}$

Has the following derivative

$y' = \frac{f'(x)}{\ln{a}*f(x)}$

In this problem, we have that:

$y = \log_{10}{\frac{3}{x}}$

So

$a = 10, f(x) = \frac{3}{x} = 3x^{-1}, f'(x) = -3x^{-2}$

The derivative of the function is:

$y' = \frac{f'(x)}{\ln{a}*f(x)}$

$y' = \frac{-3x^{-2}}{2.3*3x^{-1}}$

$y' = -\frac{1}{2.3x}$