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Question

The derivative of y=loge sin (ex) with respect to x will be

A
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B
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C
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D
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Solution

The correct option is A
It’s okay if you did not get it. Just Remember that
d(loge(x))dx=1x only if the argument of
loge is x. If not, chain rule has to be applied. Same holds for other functions as well.
Here y=loge(sin (ex))
Let’s say sin (ex)=u
ex=v

y=loge u But u is a function of v=ex and v is a function of x
So dydx=dydu×dudv×dvdx [As per chain rule]

So dydx=1u×cos v× ex

=1sin(ex)×cos(ex)× ex=cosec(ex)cos(ex)× ex

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