Chapter 3.3, Problem 3QQ

To determine

The correct option which gives the value of $\frac{dy}{dx}$ .

Answer to Problem 3QQ

The correct option is (C).

Explanation of Solution

Given information:

The expression: $y=\frac{4x-3}{2x+1}$

The options:

(A) $\frac{10}{{\left(4x-3\right)}^2}$

(B) $-\frac{10}{{\left(4x-3\right)}^2}$

(C) $\frac{10}{{\left(2x+1\right)}^2}$

(D) $-\frac{10}{{\left(2x+1\right)}^2}$

(E) 2

Calculation:

The given expression is $y=\frac{4x-3}{2x+1}$ .

Differentiate the above expression using the quotient rule $\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{u^{\prime }v-u{v}^{\prime }}{v^2}$ .

  $\begin{array}{c}\frac{dy}{dx}=\frac{4\left(2x+1\right)-2\left(4x-3\right)}{{\left(2x+1\right)}^2}\\ =\frac{8x+4-8x+6}{{\left(2x+1\right)}^2}\\ =\frac{10}{{\left(2x+1\right)}^2}\end{array}$

Hence, the correct option is (C).