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" Let f(x) " =|{:(cos x,,sin x,,cosx),(...

`" Let f(x) " =|{:(cos x,,sin x,,cosx),( cos 2x,,sin 2x,,2cos 2x),(cos 3x,,sin 3x,,3cos 3x):}|` then find the values of f'`(pi//2)`.

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`f'(x)|{:(-sin x, sin x, cos x ),(-2 sin 2x, sin 2x, 2cos 2x),(-3 sin 3x, sin 3x, 3cos 3x):}|`
`+|{:(cos x, cos x, cos x),(cos 2x, 2cos 2x, 2cos 2x),(cos 3x, 3 cos 3x, 3cos 3x):}|`
`+|{:(cos x, sin x, -sin x),(cos 2x, sin 2x, -4 sin 2x),(cos 3x, sin 3x, -9sin 3x):}|`
`=|{:(-sin x, sin x, cos x),(-2 sin 2x, sin 2x, 2 cos 2x),(-3 sin 3x, sin 3x, 3cos 3 x):}|`
`+|{:(cos x, sin x, -sin x),(cos 2 x, sin 2 x, -4 sin 2x),(cos 3x, sin 3x, -9 sin 3x):}|`
`therefore" "f'(0)=|{:(0,0,1),(0,0,2),(0,0,3):}|+|{:(1,0,0),(1,0,0),(1,0,0):}|=0+0=0`
`f'(pi//2)=|{:(-1,1,0),(0,0,-2),(3,-1,0):}|+|{:(0,1,-1),(-1,0,0),(0,-1,9):}|`
`=(-6+2)+(-1+9)=4`
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