Question

Match the given functions in the first column with their first derivatives.

• A. $\frac{1}{\sqrt{1-x^2}}$
• B. $\frac{-1}{\sqrt{1-x^2}}$
• C. $\frac{1}{1+x^2}$
• D. $\frac{-1}{\left(x\right|\sqrt{x^2-1}}$

Answer 1

The derivatives of inverse trigonometric functions are given below.

$si{n}^{-1}x\to \frac{1}{\sqrt{1-x^2}}$
$co{s}^{-1}x\to -\frac{1}{\sqrt{1-x^2}}$
$ta{n}^{-1}x\to \frac{1}{1+x^2}$
$se{c}^{-1}x\to \frac{1}{|x|\sqrt{x^2-1}}$
$co{t}^{-1}x\to \frac{-1}{1-x^2}$
$cose{c}^{-1}x\to \frac{-1}{|x|\sqrt{x^2-1}}$