JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)\) .Then, at \(x =1\),
- A \(2 y^{\prime}+\sqrt{3} \pi^2 y=0\)
- B \(2 y^{\prime}+3 \pi^2 y=0\)
- C \(\sqrt{2} y^{\prime}-3 \pi^2 y=0\)
- D \(y^{\prime}+3 \pi^2 y=0\)
Answer & Solution
Correct Answer
(B) \(2 y^{\prime}+3 \pi^2 y=0\)
Step-by-step Solution
Detailed explanation
\(y =\sin ^3(\pi / 3 \cos g(x))\) \(g(x)=\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{3 / 2}\) \(g(1)=2 \pi / 3\) \(y^{\prime}=3 \sin ^2\left(\frac{\pi}{3} \cos g(x)\right) \times \cos \left(\frac{\pi}{3} \cos g(x)\right) \times \frac{\pi}{3}(-\sin g(x)) g^{\prime}(x)\)…
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