The correct option is A x x y= x =1sin x using u/v rule. dydx=0 cos xsin^2x dydx= cos xsin x×1sinx ∴dydx= x x Hence, option ...

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Algebra of Derivatives

Differentiate...

Question

Differentiate
$csc x$

- csc x cot x

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csc x cot x

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- csc x tan x

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csc x tan x

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Solution

The correct option is A $- csc x cot x$
$y = csc x = \frac{1}{sin x}$
using $u / v$ rule.
$\frac{d y}{d x} = \frac{0 - cos x}{{sin}^{2} x}$

$\frac{d y}{d x} = \frac{- cos x}{sin x} \times \frac{1}{s i n x}$
$∴ \frac{d y}{d x} = - cot x csc x$
Hence, option A.

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