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If y = cos2 x2, find \(\frac {dy}{dx}\)1. 4x2 sin x2 cos x22. -4x cos x2 sin x23. 2x sin x2 cos x24. -2x cos x2 sin x2 |
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Answer» Correct Answer - Option 2 : -4x cos x2 sin x2 Concept: cos2x = 2cos2x - 1 sin2x = 2sin x cos x
Calculation: Here, y = cos2 x2 Let, x2 = t Differentiating with respect to x, we get ⇒2xdx = dt ⇒ dt/dx = 2x ....(1) y = cos2t =\(\rm \frac{\cos2t+1}{2}=\frac{\cos2t}{2}+\frac{1}{2}\) \(\rm \frac{dy}{dx} = \frac{1}{2}\frac{d}{dt}(\cos2t)\frac{dt}{dx}+0\\ = \frac{1}{2}(-2\sin2t)\frac{dt}{dx}\cdots (from \ (1))\) = - sin2x2 × 2x = -4x cos x2 sin x2 Hence, option (2) is correct. |
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