Match List - I with List - II.
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List – I (Function y) |
List – II (Derivative $\frac{dy}{dx}$) |
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(A) |
$y=\cos \sqrt{x}$ |
(I) |
$\frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}$ |
|
(B) |
$y=\sqrt{\sin x}$ |
(II) |
$-3 x^2 \cos \left(x^3\right) \sin \left(\sin \left(x^3\right)\right)$ |
|
(C) |
$y=\sec (\tan \sqrt{x})$ |
(III) |
$\frac{\cos x}{2 \sqrt{\sin x}}$ |
|
(D) |
$y=\cos \left(\sin \left(x^3\right)\right)$ |
(IV) |
$\frac{-1}{2 \sqrt{x}} \sin \sqrt{x}$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
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Functions |
Their Derivatives |
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(A) |
$y=\cos \sqrt{x}$ |
$y' = \frac{-\sin \sqrt{x}}{2 \sqrt{x}}$ → (IV) |
|
(B) |
$y=\sqrt{\sin x}$ |
$y' = \frac{\cos x}{2 \sqrt{\sin x}}$ → (III) |
|
(C) |
$y=\sec (\tan \sqrt{x})$ |
$y' = \frac{\sec (\tan \sqrt{x}) \tan (\tan \sqrt{x}) \sec ^2 \sqrt{x}}{2 \sqrt{x}}$ → (I) |
|
(D) |
$y=\cos \left(\sin \left(x^3\right)\right)$ |
$y' = -\sin \left(\sin \left(x^3\right)\right) \cos \left(x^3\right) (3 x^2)$ → (II) |