Question

differentiate log sin x using first principle. Show the steps properly.

Answer 1

Hey here is your answer
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$let \: y \: = \: ln( \sin(x) ) \\ \\ then \: . \\ \\ \frac{dy}{dx} = \frac{d \: ( ln( \sin(x) ) }{dx} \: \: \: by \: chain \: rule \\ \\ = \frac{d \: ln( \sin(x) ) }{d \: \sin(x) } \times \frac{ d \: \sin(x) }{dx} \\ \\ = \frac{1}{ \sin(x) } \times \cos(x) \\ \\ = \cot(x)$
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