COMEDK · Maths · 26. Differentiation
The second derivative of \(\sin 3x \cos 5x\) is:
- A \(2\sin 2x + 16\sin 8x\)
- B \(2\sin 2x + 32\sin 8x\)
- C \(2\sin 2x - 32\sin 8x\)
- D \(2\sin 2x - 16\sin 8x\)
Answer & Solution
Correct Answer
(C) \(2\sin 2x - 32\sin 8x\)
Step-by-step Solution
Detailed explanation
Let \(y = \sin 3x \cos 5x\) Using the identity \(2 \sin A \cos B = \sin(A+B) + \sin(A-B)\), we get: \(y = \dfrac{1}{2} [\sin(3x+5x) + \sin(3x-5x)]\) \(y = \dfrac{1}{2} [\sin 8x + \sin(-2x)]\) \(y = \dfrac{1}{2} [\sin 8x - \sin 2x]\) Differentiating with respect to \(x\):…
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