Question

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

Options

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

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

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

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

Answer 1

The derivative of \[\tan^{-1}(f(x))\] has denominator \[1+\{f(x)\}^{2}\]. It is multiplied by \[\frac{d}{dx}f(x)\] for \[f(x)\in\mathbb{R}\].