AP EAMCET · Maths · Differentiation
If \(x=\sqrt{2} e^t(\sin t-\cos t)\) and \(y=\sqrt{2} e^t(\sin t+\cos t)\), then \(\left(\frac{d^2 y}{d x^2}\right)t=\frac{\pi}{4}=\)
- A \(-\mathrm{e}^{-\pi / 4}\)
- B \(\sqrt{2} \mathrm{e}^{\pi / 4}\)
- C \(\sqrt{2} \mathrm{e}^{-\pi / 4}\)
- D \(\mathrm{e}^{-\pi / 4}\)
Answer & Solution
Correct Answer
(A) \(-\mathrm{e}^{-\pi / 4}\)
Step-by-step Solution
Detailed explanation
\(\frac{dx}{dt} = \sqrt{2} (e^t(\sin t - \cos t) + e^t(\cos t + \sin t)) = 2\sqrt{2}e^t \sin t\) \(\frac{dy}{dt} = \sqrt{2} (e^t(\sin t + \cos t) + e^t(\cos t - \sin t)) = 2\sqrt{2}e^t \cos t\)…
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