TS EAMCET · Maths · Differentiation
If \(y=a \cos 3 x+b e^{-x}\), then \(y^{\prime \prime}(3 \sin 3 x-\cos 3 x)=\)
- A \(10 y^{\prime} \sin 3 x+3 y(\sin 3 x+3 \cos 3 x)\)
- B \(10 y^{\prime} \cos 3 x+3 y(\sin 3 x+3 \cos 3 x)\)
- C \(10 y^{\prime} \cos 3 x+3 y(\cos 3 x+3 \sin 3 x)\)
- D \(10 y^{\prime} \cos 3 x+3 y(\sin 3 x-3 \cos 3 x)\)
Answer & Solution
Correct Answer
(B) \(10 y^{\prime} \cos 3 x+3 y(\sin 3 x+3 \cos 3 x)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } y=a \cos 3 x+b e^{-x} \\ & y^{\prime}=-3 a \sin 3 x-b e^{-x} ; y^{\prime \prime}=-9 a \cos 3 x+b e^{-x} \\ & \text { Now, } y^{\prime \prime}(3 \sin 3 x-\cos 3 x) \\ & =\left(-9 a \cdot \cos 3 x+b e^{-x}\right)(3 \sin 3 x-\cos 3 x) \\ & =-27 a \cos 3…
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