MHT CET · Maths · Differentiation
If \(y=\cos ^2\left(\frac{5 x}{2}\right)-\sin ^2\left(\frac{5 x}{2}\right)\), then \(\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=\)
- A -25y
- B \(\frac{25}{2} y\)
- C \(-\frac{25}{2} y\)
- D 25y
Answer & Solution
Correct Answer
(A) -25y
Step-by-step Solution
Detailed explanation
\(y=\cos ^2 \frac{5 x}{2}-\sin ^2 \frac{5 x}{2}=\cos 5 x\)
\(\Rightarrow \frac{\mathrm{d} y}{\mathrm{~d} x}=-5 \sin 5 x\)
\(\Rightarrow \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=-25 \cos 5 x=-25 y\)
\(\Rightarrow \frac{\mathrm{d} y}{\mathrm{~d} x}=-5 \sin 5 x\)
\(\Rightarrow \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}=-25 \cos 5 x=-25 y\)
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