Differentiate y= log (sin x ) w.r.t x .

Answers (1)

Solution:  We have , 

                                  y= log (sinx)

putting u=sinx , we get 

                                  y=log u and u=sinx 

	herefore                               fracmathrmdy mathrmd u=frac1u           and      fracmathrmdu mathrmd x=cosx.

Now ,                         fracmathrmdy mathrmd x=fracmathrmd ymathrmd u	imes fracmathrmd umathrmd x

Rightarrow                             fracmathrmd ymathrmd x=frac1u	imes cosx =frac1sinx	imes cosx=cotx.

Hence ,                    fracmathrmd log(sinx) mathrmd x=cotx.

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