AP EAMCET · Maths · Differentiation
If \(f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1\end{array}\right|\), then the value of \(f^{\prime}(x)\) at \(x=0\) is equal to
- A -1
- B 1
- C 2
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } f(x)=\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1 \end{array}\right| \\ & \therefore \quad f^{\prime}(x)=\left|\begin{array}{ccc} -\sin x & 1 & 0 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1…
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