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Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation2 Marks
MCQ
If $y=\cos ^2\left(\frac{5 x}{2}\right)-\sin ^2\left(\frac{5 x}{2}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to
  • A
    $-5 \sqrt{1-y^2}$
  • B
    $25 y$
  • ✓
    $-25 y$
  • D
    $25 \sqrt{1-y^2}$
✓

Answer

Correct option: C.
$-25 y$
Given, $y=\cos ^2\left(\frac{5 x}{2}\right)-\sin ^2\left(\frac{5 x}{2}\right)$
$\Rightarrow y=\cos 5 x$
$ \Rightarrow \frac{d y}{d x}=-5 \sin 5 x $
$\Rightarrow \frac{d^2 y}{d x^2}=-5 \times 5 \cos 5 x$
$=-25 \cos 5 x=-25 y$

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