What is the derivative of tan^-1(cot(sqrt(x)))?
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We have the function f(x) = arc tan ( cot ( sqrt x)) and we have to find the derivative of f(x).
arc tan ( cot ( sqrt x))
we know that cot x = tan ( pi/2 - x)
=> arc tan ( tan ( pi/2 - sqrt x))
=> pi/2 - sqrt x
f(x) = pi/2 - sqrt x
=> f(x) = pi/2 - x^(1/2)
f'(x) = 0 - (1/2)* x^(1/2 - 1)
=> -(1/2) x^(-1/2)
=> -1 / 2*sqrt x
The required derivative is -1/(2*sqrt x)
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