Question

Match the following functions to their derivatives?
$\begin{array}{cc}Function& Derivatives\\ a)si{n}^{-1}x& 1)\frac{-1}{|x|\sqrt{x^2-1}}\\ b)co{s}^{-1}x& 2)\frac{-1}{1+x^2}\\ c)ta{n}^{-1}x& 3)\frac{1}{|x|\sqrt{x^2-1}}\\ d)se{c}^{-1}x& 4)\frac{1}{1+x^2}\\ e)co{t}^{-1}x& 5)\frac{-1}{\sqrt{1-x^2}}\\ f)cose{c}^{-1}x& 6)\frac{1}{\sqrt{1-x^2}}\end{array}$

• A. a-6, b-5, c-4, d-3, e-2, f-1
• B. a-5, b-6, c-4, d-3, e-2, f-1
• C. a-6, b-5, c-3, d-4, e-2, f-1
• D. a-6, b-5, c-3, d-2, e-1, f-2

Answer 1

The correct option is A a-6, b-5, c-4, d-3, e-2, f-1

Try to recall that all the functions mentioned in the questions are standard inverse trigonometric functions whose derivatives were mentioned in the videos. In case you forgot some, following are the derivatives.
$si{n}^{-1}x=\frac{1}{\sqrt{1-x^2}}$
$co{s}^{-1}x=-\frac{1}{\sqrt{1-x^2}}$
[This is -1 times the derivative of $si{n}^{-1}$]
$ta{n}^{-1}x=\frac{1}{1+x^2}$
$se{c}^{-1}x=\frac{1}{|x|\sqrt{x^2-1}}$
$co{t}^{-1}x=\frac{-1}{1-x^2}$
[This is -1 times the derivative of $ta{n}^{-1}$]
$cose{c}^{-1}x=\frac{-1}{|x|\sqrt{x^2-1}}$
[This is -1 times the derivative of $se{c}^{-1}$]
Try to remember them as it will save your time in problem solving.