Let y = ( x^2), then the value of dy/dx at x = sqrt()2 is equal to Option 1: -sqrt()2(1sqrt(2)) Option 2: -sqrt(/2)(1sqrt(2)) Option 3: -sqrt(/2)(1sqrt(2)) Option 4: sqrt(/2)(1sqrt(2))

The answer is '-sqrt(/2)(1sqrt(2))'. View full solution:

Calculus > Continuity & Differentiability

Medium

core

Let $y = \sin(\cos x^2)$, then the value of $\frac{dy}{dx}$ at $x = \frac{\sqrt{\pi}}{2}$ is equal to

$-\frac{\sqrt{\pi}}{2}\cos\left(\frac{1}{\sqrt{2}}\right)$

$-\sqrt{\frac{\pi}{2}}\cos\left(\frac{1}{\sqrt{2}}\right)$

$-\sqrt{\frac{\pi}{2}}\sin\left(\frac{1}{\sqrt{2}}\right)$

$\sqrt{\frac{\pi}{2}}\sin\left(\frac{1}{\sqrt{2}}\right)$

✅ Correct Option: 2

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