Let y = cos(tan ) dx = -sin(tan ). ) dx = -sin(tan ).sec 2 . ) dx =-sin(tan ).sec 2 . 2 therefore, dx = - 2 sin(tan ).sec 2 .

class 12 maths continuity and differentiability

cos(tan$\sqrt{x+1}$ )

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📘 Continuity and Differentiability NCERT Exemp. Ex.5.3 ,Q.31,Page 109 SA

Official Solution

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Let $y = cos(tan\sqrt{x+1})$

$\frac{dy}{dx} = -sin(tan\sqrt{x+1}). \frac{d(tan\sqrt{x+1})}{dx}$

$= -sin(tan\sqrt{x+1}).sec^2\sqrt{x+1}.\frac{d(\sqrt{x+1})}{dx}$

$=-sin(tan\sqrt{x+1}).sec^2\sqrt{x+1}.\frac{1}{2\sqrt{x+1}}$

therefore, $\frac{dy}{dx} = -\frac{1}{2\sqrt{x+1}}sin(tan\sqrt{x+1}).sec^2\sqrt{x+1}.$

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