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Question
Differentiate the following with respect to x.
(sin x)tan x
Solution
Let y = (sin x)tan x
Taking logarithm on both sides we get,
log y = tan x log(sin x)
Differentiating with respect to x,
`1/y "dy"/"dx" = tan x "d"/"dx"` (log (sin x)) + log (sin x) `"d"/"dx"` (tan x)
= tan x `1/(sin x)`(cos x) + log (sin x) sec2x
`1/y "dy"/"dx" = (sin x)/(cos x) xx (cos x)/(sin x)` + log (sin x)(sec2x)
= 1 + log (sin x)(sec2x)
`"dy"/"dx"` = y[1 + sec2x log (sin x)]
= (sin x)tan x[1 + sec2x log (sin x)]
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