Find the derivatives of the following functions with respect to corresponding independent variables: y = cosec x . cot x

Find the derivatives of the following functions with respect to corresponding independent variables:

y = cosec x . cot x

बेरीज

y = u v

⇒ y’ = uv’ + vu’

u = cosec x

⇒ u’ = – cosec x cot x

v = cot x

⇒ v’ = – cosec² x

`("d"y)/("d"x)` = (cosec x)(– cosec²x) + cot x(– coseç x cot x)

= cosec³x – cosec x cot²x

= – cosec x (cosec²x + cot²x)

= `- 1/sinx (1/(sin^2x)+ (cos^2x)/(sin^2x))`

= `- ((1 + cos^2x))/(sinx sin^2x)`

= `- ((1 + cos^2x))/(sin^x)`

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Differentiation Rules

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पाठ 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.2 [पृष्ठ १६०]

पाठ 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.2 | Q 14 | पृष्ठ १६०

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