differentiation of log e with base x - Maths - Application of Derivatives

Question

differentiation of log e with base x?

Shridhar Kaushik · Accepted Answer

We have to differentiate logxe w r t 'x' $Let y = \log_{x} e = \frac{1}{\log_{e} x} [{∵ \log}_{a} b = \frac{1}{\log_{b} a}] \Rightarrow y = {(\log_{e} x)}^{- 1}$ Differentiating both sides w r t 'x', we get $\frac{d y}{d x} = - 1 \times (\log_{e} x)^{- 2} \times \frac{1}{x} \Rightarrow \frac{d y}{d x} = \frac{- 1}{x (\log_{e} x)^{2}}$