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Choose the correct option.
The derivative of log x with respect to 1/x is:
The derivative of $\log x$ with respect to $\frac{1}{x}$ is:
- (a)$\frac{1}{x}$
- (b)$-\frac{1}{x^3}$
- (c)$-\frac{1}{x}$
- (d)$-x$
Answer
Answer
Correct option: (d)
Answer: (d) $-x$
Let $u = \log x$, $v = \frac{1}{x}$. Then $\frac{du}{dx} = \frac{1}{x}$, $\frac{dv}{dx} = -\frac{1}{x^2}$.
$\frac{du}{dv} = \frac{1/x}{-1/x^2} = -x$.