Question

Match the following

$\begin{array}{cc}Functions& Derivatives\\ \left(a\right)\sin x& 1)-\sin x\\ \left(b\right)\cos x& 2){\sec }^{2}x\\ \left(c\right)\tan x& 3)\cos x\\ \left(d\right)\sec x& 4)-cose{c}^{2}x\\ \left(e\right)\cot x& 5)\sec x\tan x\\ \left(f\right)cosecx& 6)-cosecxcotx\end{array}$

• A. a – 1, b – 3, c – 2, d – 4, e – 5, f – 6
• B. a – 3, b – 1, c – 2, d – 5, e – 4, f – 6
• C. a – 2, b – 1, c – 3, d – 5, e – 4, f – 6
• D. None of the above

Answer 1

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

As mentioned in the videos, the derivatives of trigonometric functions are as follows.
$\sin x\to \cos x\cos x\to -\sin x\tan x\to {\sec }^{2}x\sec x\to \sec x\tan x\cot x\to -{\text{cosec}}^{2}x\text{cosec}x\to -\text{cosec}x\cot x$
For problem solving and to save the time they should be remembered. In case you forget any of them, you can use the first principle to evaluate the derivative.