TS EAMCET · Maths · Differentiation
If \(y=a \cos (\sin 2 x)+b \sin (\sin 2 x)\), then \(y^{\prime \prime}+(2 \tan 2 x) y^{\prime}\) is equal to
- A 0
- B \(4\left(\cos ^2 2 x\right) y\)
- C \(-4\left(\cos ^2 2 x\right) y\)
- D \(-\left(\cos ^2 2 x\right) y\)
Answer & Solution
Correct Answer
(C) \(-4\left(\cos ^2 2 x\right) y\)
Step-by-step Solution
Detailed explanation
Given, \[ y=a \cos (\sin 2 x)+b \sin (\sin 2 x) \] On differentiating both sides w.r.t. \(x\), we get \[ \begin{aligned} y^{\prime}=-a & \sin (\sin 2 x) \cos 2 x \cdot 2 \\ & +b \cos (\sin 2 x) \cdot(\cos 2 x) \cdot 2 \end{aligned} \]…
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