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Question

If f(x)=∣ ∣ ∣2cosx10xπ22cosx1012cosx∣ ∣ ∣ then dfdx at x=π2 is

A
2
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B
π2
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C
1
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D
8
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Solution

The correct option is A 2
f(x)=∣ ∣ ∣2cosx10xπ22cosx1012cosx∣ ∣ ∣
(Expanding along first column)
=2cosx(4cos2x1)(xπ2)(2cosx0)
=8cos3x2cosx2xcosx+πcosx
f(x)=24cos2x(sinx)+2sinx2(cosxxsinx)πsinx
f(π2)=0+2+0=2

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