Question

Which expression is the derivative of \[\cos^{-1}(f(x))\] when \[|f(x)|<1\]?

Options

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

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

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

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

Answer 1

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