Question

The derivative of log x with respect to `1/x` is ______.

विकल्प

• `1/x`

• `(-1)/x^3`

• `(-1)/x`

• – x

Answer 1

The derivative of log x with respect to `1/x` is – x.

Explanation:

Let u = log x

and v = `1/x`

Differentiate w.r. to ‘x’

`(du)/dx = 1/x`

and `(dv)/dx = (-1)/x^2`

and `(du//dx)/(dv//dx) = (1/x)/((-1)/x^2)`

`\implies (du)/(dv)` = – x