AP EAMCET · Maths · Differentiation
If \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\), then \(\frac{d^2 y}{d x^2}\) at \(\theta=\frac{\pi}{4}\) is
- A \(\frac{4 \sqrt{2}}{39}\)
- B \(\frac{2}{3 a}\)
- C \(\frac{2 \sqrt{2}}{3 a}\)
- D \(\frac{7 \sqrt{2}}{3 a}\)
Answer & Solution
Correct Answer
(A) \(\frac{4 \sqrt{2}}{39}\)
Step-by-step Solution
Detailed explanation
We are given that \(x=a \cos ^3 \theta, y=a \sin ^3 \theta\) Now \(\frac{d x}{d \theta}=3 a \cos ^2 \theta(-\sin \theta), \frac{d y}{d \theta}=3 a \sin ^2 \theta(\cos \theta)\) Now,…
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