Question

# If ( y=log (sin x), ) then find ( frac{d y}{d x} )

Solution

( y=log (sin x) )

( frac{d y}{d x}=frac{1}{sin x} cos x )

( frac{d y}{d x}=frac{cos x}{sin x}=cot x )

( begin{array}{l}y=log (sin x) operatorname{lot} sin x=2 y=log 2 frac{d y}{d z}=frac{1}{z} & frac{d z}{d x}=frac{d(sin x)}{d x}=cos x text { and } frac{d y}{d x} times frac{d z}{d x} Rightarrow frac{d y}{d x}=frac{1}{z} times cos x = & frac{cos x}{sin x} = & cot xend{array} )