KCET · Maths · Differentiation
If \( [x] \) represents the greatest integer function and \( f(x)=x-[x]-\cos x \) then \( f^{\prime}\left(\frac{I}{2}\right)= \)
- A \( 11 \)
- B does not exist
- C \( 00 \)
- D \( 2 \)
Answer & Solution
Correct Answer
(D) \( 2 \)
Step-by-step Solution
Detailed explanation
(D)
\[
\begin{array}{l}
f(x)=x-[x]-\cos x \\
f^{\prime}(x)=1+\sin x \\
f^{\prime}\left(\frac{\Pi}{2}\right)=1+1=2
\end{array}
\]
\[
\begin{array}{l}
f(x)=x-[x]-\cos x \\
f^{\prime}(x)=1+\sin x \\
f^{\prime}\left(\frac{\Pi}{2}\right)=1+1=2
\end{array}
\]
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