AP EAMCET · Maths · Differentiation
If \(y=\cos ^{-1}(\cos x)\), then find \(\frac{d y}{d x}\) at \(x=\frac{5 \pi}{4}\)
- A 1
- B -1
- C 0
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(B) -1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & y=\cos ^{-1}(\cos x) \\ & y=\cos ^{-1}(\cos (2 \pi-x)) \quad[\because x \in(\pi, 2 \pi)]\end{aligned}\) \(\begin{aligned} y & =2 \pi-x \\ \frac{d y}{d x} & =-1\end{aligned}\)
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