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If f(x) = tan^(-1) ((2cot^(2)x)/(1 + cos^(2)x)) then d/(dx) (f(f(x))) at x = pi/2 is |
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Answer» Solution :`f(x) = TAN^(-1)((2cot^2 x)/(1+cos^2 x))` `= tan^(-1)((2 cos^2 x)/(1-cos^4 x))` `=2 tan^(-1)(cos^(2)x)` `f'(x) = (-2)/(1+cos^4 x) [ 2 sin x cos x]` `f'(x) = (4 sin x. Cos x)/(1 + sin^4 x)` `f' ((pi)/2) = 0` `d/(dx) f(f(x)) - f'(f(x)) f'(x)` `d/(dx) f(f(x))` at `(x - pi/2) = f'(f((pi)/2))f'(pi/2) = 0`. |
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