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[f(x)=x^(50)-x^(20)" in "[0,1].],[f(x)=c...

[f(x)=x^(50)-x^(20)" in "[0,1].],[f(x)=cos^(2)x+sin x]

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f_(1)(x)=sin^(-1)(cos(sin^(2)x)),f_(2)(x)=cos^(-1)(sin(cos^(2)x)),f_(3)(x)=sin^(-1)(cos^(2)x)),f_(4)(x)=cos^(-1)(sin^(2)x)* Then which of the following is/are correct?

If 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)sin2x0sin2x^2|,t h e n f(-2)=0 (b) f^(prime)(-1/2)=0 f^(prime)(-1)=-2 (d) f^(0)=4

If 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)sin2x0sin2x^2|,t h e n f(-2)=0 (b) f^(prime)(-1/2)=0 f^(prime)(-1)=-2 (d) f^(0)=4

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) .

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) .

If 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,sin2x^2]| then find f'(x)

If f(x) = |(1+sin^(2)x,cos^(2)x,4 sin 2x),(sin^(2)x,1+cos^(2)x,4 sin 2x),(sin^(2)x,cos^(2)x,1+4 sin 2x)| What is the maximum value of f(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))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"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).

"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).