First slide

Derivatives

Question

$If y = \cot^{- 1} [\tan (\frac{π}{2} - x)] then \frac{d y}{d x} =$

Easy

A

x
B

1
C

$\frac{1}{1 + x^{2}}$
D

$\frac{- 1}{1 + x^{2}}$

Solution

$y = \cot^{- 1} [\tan (\frac{π}{2} - x)] = C o t^{- 1} \cot x = x \Rightarrow \frac{d y}{d x} = 1.$

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