Answer:
[tex]y' = -\frac{1}{2.3x}[/tex]
Step-by-step explanation:
The derivative of [tex]a*x^{n}[/tex] is [tex]a*n*x^{n-1}[/tex]. The derivative of [tex]3x^{-1}[/tex] is [tex]-3x^{-2}[/tex], for example.
Derivative of the log function:
[tex]y = \log_{a}{f(x)}[/tex]
Has the following derivative
[tex]y' = \frac{f'(x)}{\ln{a}*f(x)}[/tex]
In this problem, we have that:
[tex]y = \log_{10}{\frac{3}{x}}[/tex]
So
[tex]a = 10, f(x) = \frac{3}{x} = 3x^{-1}, f'(x) = -3x^{-2}[/tex]
The derivative of the function is:
[tex]y' = \frac{f'(x)}{\ln{a}*f(x)}[/tex]
[tex]y' = \frac{-3x^{-2}}{2.3*3x^{-1}}[/tex]
[tex]y' = -\frac{1}{2.3x}[/tex]
