What is the derivative of f(x) = (7x/(2x -1)(x+3)) ?

Question

What is the derivative of f(x) = (7x/(2x -1)(x+3)) ? (A) - (3/(x + 3)2) - (2/(2x - 1)2) (B) - (3/(x + 3)2) - (1/(2x - 1)2) (C)  (3/(x + 3)2) + (1/(2x - 1)2) (D)  (3/(x + 3)2) + (2/(2x - 1)2)

Tardigrade Admin · Accepted Answer

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

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

$- \frac{3}{( x + 3 ) ^{2}} - \frac{2}{( 2 x - 1 ) ^{2}}$

$- \frac{3}{( x + 3 ) ^{2}} - \frac{1}{( 2 x - 1 ) ^{2}}$

$\frac{3}{( x + 3 ) ^{2}} + \frac{1}{( 2 x - 1 ) ^{2}}$

$\frac{3}{( x + 3 ) ^{2}} + \frac{2}{( 2 x - 1 ) ^{2}}$

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

Q. What is the derivative of f(x)=(2x−1)(x+3)7x​?

−(x+3)23​−(2x−1)22​

−(x+3)23​−(2x−1)21​

(x+3)23​+(2x−1)21​

(x+3)23​+(2x−1)22​