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JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f(x)\, = sin\, (sin\,x)\) and \(f"(x) + tan\,xf'(x) + g(x)\, = 0\), then \(g(x)\) is
- A \(cos^2\, x\, cos\, (sin\, x)\)
- B \(sin^2\,x\, cos\, (cos\,x)\)
- C \(sin^2\, x\, sin (cos\,x)\)
- D \(cos^2\, x\, sin\, (sin\,x)\)
Answer & Solution
Correct Answer
(D) \(cos^2\, x\, sin\, (sin\,x)\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = \sin \left( {\sin x} \right)\) \( \Rightarrow f'\left( x \right) = \cos \left( {\sin x} \right).\cos x\) \( \Rightarrow f''\left( x \right) = - \sin \left( {\sin x} \right).{\cos ^2}x + \cos \left( {\sin x} \right).\left( { - \sin x} \right)\)…
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