Question

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

y = log10 3/x

Answer 1

`y' = -(1)/(2.3x)`

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' = (f'(x))/(ln(a)*f(x))`

In this problem, we have that:

`y = \log_(10){(3)/(x)}`

So

`a = 10, f(x) = (3)/(x) = 3x^(-1), f'(x) = -3x^(-2)`

The derivative of the function is:

`y' = (f'(x))/(ln(a)*f(x))`

`y' = (-3x^(-2))/(2.3*3x^(-1))`

`y' = -(1)/(2.3x)`