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Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
Differential coefficient of $\sqrt{\sec \sqrt{x}}$ is
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Answer

$(b) :$ Let $y=\sqrt{\sec \sqrt{x}}$
Differentiating w.r.t. $x$, we get
$\frac{d y}{d x}=\frac{1}{2 \sqrt{\sec \sqrt{x}}} \cdot \sec \sqrt{x} \cdot \tan \sqrt{x} \cdot \frac{1}{2 \sqrt{x}}$
$=\frac{1}{4 \sqrt{x}}(\sec \sqrt{x})^{1 / 2} \frac{\sin \sqrt{x}}{\cos \sqrt{x}}=\frac{1}{4 \sqrt{x}}(\sec \sqrt{x})^{3 / 2} \cdot \sin \sqrt{x}$

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