Question

Please help!

Answer 1

Differentiate
\[y=\cot ^{-1}(\sqrt{x+1})\]

Answer 2

\[y'= \frac{ -1 }{ 1+\sqrt{(X+1)}^2 } \times (\frac{ 1 }{ 2 }(X+1)^{-1/2})\]
\[y' = \frac{ -1 }{ 1+(X+1) } \times \frac{ 1 }{ 2\sqrt{X+1} }\]
\[y' = \frac{ -1 }{ X+2 } \times \frac{ 1 }{ 2\sqrt{X+1} }\]
\[y' = \frac{ -1 }{ 2(X+2)\sqrt{X+1} } \] or
\[y'=\frac{ -1 }{ (2X+4)\sqrt{X+1} }\]

Answer 3

This is the best I can do, please verify and/or check the workings yourself if possible. I hope this may help you.