Question

Which expression is the derivative of \[\cot^{-1}(f(x))\] when \[f(x)\in\mathbb{R}\]?

Options

• \[-\frac{1}{\sqrt{1-\{f(x)\}^{2}}}\frac{d}{dx}f(x)\]

• \[-\frac{1}{1+\{f(x)\}^{2}}\frac{d}{dx}f(x)\]

• \[\frac{1}{1+\{f(x)\}^{2}}\frac{d}{dx}f(x)\]

• \[-\frac{1}{|f(x)|\sqrt{\{f(x)\}^{2}-1}}\frac{d}{dx}f(x)\]

Answer 1

The derivative of \[\cot^{-1}(f(x))\] is negative. Its denominator is \[1+\{f(x)\}^{2}\], and it includes \[\frac{d}{dx}f(x)\].