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Question
Differentiate the following with respect to x.
(sin x)x
Solution
Let y = (sin x)x
Taking logarithm on both sides we get,
log y = x log(sin x)
Differentiating with respect to x,
`1/y * "dy"/"dx" = x "d"/"dx" log(sin x) + log(sin x) "d"/"dx" (x)`
`1/y * "dy"/"dx" = x1/(sin x) (cos x) + log(sin x)(1)`
`1/y * "dy"/"dx"` = x cot x + log(sin x)
`"dy"/"dx"` = y[x cot x + log(sin x)]
`"dy"/"dx"`= (sin x)x [x cot x + log(sin x)]
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