Question(a) Write the difference quotient for $f(x)=\ln x$. $$\frac{f(x+h)-f(x)}{h}=$$

Studdy Solution
Simplify the expression:
Using the properties of logarithms, we know that:
$$\ln(x+h) - \ln x = \ln\left(\frac{x+h}{x}\right)$$
So, the difference quotient becomes:
$$\frac{\ln\left(\frac{x+h}{x}\right)}{h}$$
The difference quotient for $f(x) = \ln x$ is:
$$\frac{\ln\left(\frac{x+h}{x}\right)}{h}$$