Differentiate y=log( cosecx) find dy/dx - Maths - Continuity and Differentiability

Question

Differentiate
y=log( cosecx) find dy/dx

Gursheen kaur. · Accepted Answer

y = log(cosecx)

Putting u = cosecx , we get ,

y = log u and u = cosec x

∴ $\frac{d y}{d u} = \frac{1}{u} a n d \frac{d u}{d x} = - \cos e c x . \cot x$

$N o w, \frac{d y}{d x} = \frac{d y}{d u} . \frac{d u}{d x} \Rightarrow \frac{d y}{d x} = \frac{1}{u} . (- \cos e c x . \cot x) \Rightarrow \frac{d y}{d x} = \frac{1}{\cos e c x} . (- \cos e c x . \cot x) \Rightarrow \frac{d [\log (\cos e c x)]}{d x} = - \cot x$

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