Question

What is the derivative of $f(x) = \frac{7x}{(2x -1)(x+3)} ?$

• A. $- \frac{3}{(x + 3)^2} - \frac{2}{(2x - 1)^2}$
• B. $- \frac{3}{(x + 3)^2} - \frac{1}{(2x - 1)^2}$
• C. $ \frac{3}{(x + 3)^2} + \frac{1}{(2x - 1)^2}$
• D. $ \frac{3}{(x + 3)^2} + \frac{2}{(2x - 1)^2}$

Answer 1

Answer: (A)

Given function is $f(x) = \frac{7x}{(2x -1)(x+3)} $
Breaking into partial fraction
We get, $f(x) = \frac{1}{2x - 1} + \frac{3}{x + 3}$
Differentiating w.r.t. x, we get
$f'(x) = - \frac{2}{(2x -1)^2} - \frac{3}{(x + 3)^2}$