Differentiation of log x w.r.t \(\displaystyle\frac{1}{x}\) is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-x\)
Let \(u=\log x\) and \(v=\frac{1}{x}\). The derivative of u with respect to v is
\( \displaystyle \frac{du}{dv}=\frac{du/dx}{dv/dx} \)
\( \displaystyle \frac{du}{dx}=\frac{1}{x},\quad \frac{dv}{dx}=-\frac{1}{x^2} \)
\( \displaystyle \frac{du}{dv}=\frac{1/x}{-1/x^2}=-x \)