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"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)...

`"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|.`
Find the value of f'(0).

Text Solution

Verified by Experts

The correct Answer is:
2
Since in `R_(3)`, putting x=0, all the elements are zero then
`f'(0)=0+0+|{:(1,0,-1),(0,1,0),(2 cos 0,0, 4(0)cos 0):}|=|{:(1,0,-1),(0,1,0),(2,0,0):}|=2`
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