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Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+...

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)],[sin2x,0,sin(2x^2)]|` . Find the value of `f^(prime)(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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