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प्रश्न
The derivative of log x with respect to `1/x` is ______.
विकल्प
`1/x`
`(-1)/x^3`
`(-1)/x`
– x
उत्तर
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
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