TS EAMCET · Maths · Differentiation
If \(x=\cos ^3 \theta-\sin ^3 \theta\) and \(y=\sqrt[3]{\cos \theta}-\sqrt[3]{\sin \theta}\), then the the value of \(\frac{d y}{d x}\) at \(\theta=\frac{\pi}{4}\) is
- A \(\frac{2}{9} \sqrt[3]{2}\)
- B \(\frac{\sqrt[3]{2}}{3}\)
- C \(\frac{4}{9} \sqrt[3]{2}\)
- D \(\frac{\sqrt[3]{2}}{9}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{9} \sqrt[3]{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {} x=\cos ^3 \theta-\sin ^3 \theta \\ & \frac{d x}{d \theta}=-3 \cos ^2 \theta \sin \theta-3 \sin ^2 \theta \cdot \cos \theta\end{aligned}\)…
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