# Find the derivative of $f(x)=\frac{1}{\ln x}$ and approximate $f'(3.00)$ to 4 decimals.

Find the derivative of $f(x)=\frac{1}{\ln x}$ and approximate $f'(3.00)$ to 4 decimals.

I've been having trouble with this one for a while, I've been using quotient rule but I keep getting 3 when the answer should be a decimal answer

How do I solve it?

Noting that $f(x) = \left(\ln{x}\right)^{-1}$, we see that
$$f'(x) = -\left(\ln{x}\right)^{-2} \cdot \frac{1}{x} = -\frac{1}{x(\ln{x})^2}$$
Hence $$f'(3) = \frac{-1}{3(\ln{3})^2}$$