Question

Match the following with the functions in List $1$ and their derivatives in List $2$:

Answer 1

A. Differentiate the given function with respect to $x$.
$\frac{d}{dx}\left(\sin x\right)=\cos x$
Hence, $A\to 4$
B. Differentiate the given function with respect to $x$.
$\frac{d}{dx}\left(x^{-4}\right)=-4x^{(-4-1)}$
$\Rightarrow \frac{d}{dx}{x}^{-4}=-4x^{-5}$
Hence, $B\to 1$
C. Differentiate the given function with respect to $x$.
$\frac{d}{dx}\left(\frac{2}{\sec x}\right)=\frac{-2\tan x}{\sec x}$
$\Rightarrow \frac{d}{dx}\frac{2}{\sec x}=-2\sin x.$
Hence, $C\to 2$.
D. Differentiate the given function with respect to $x$.
$\frac{d}{dx}\left(3x^3\right)=9x^{(3-1)}$
$\Rightarrow \frac{d}{dx}3x^3=9x^2$
Hence, $D\to 3$