Find the derivative of $f ( x ) = \frac { x } { x ^ { 2 } + 3 }$ .
A) $\frac { 1 } { 2 x + 3 }$

B) $\frac { - 3 + x ^ { 2 } } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
C) $\frac { 3 - x ^ { 2 } } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
D) $\frac { 3 - x ^ { 2 } } { \left( x ^ { 2 } + 3 \right) }$
E) $\frac { 3 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
F) $\frac { 1 } { 2 x }$

G) $\frac { 3 - x } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

H)None of these

Question

Find the derivative of $f ( x ) = \frac { x } { x ^ { 2 } + 3 }$ .
A) $\frac { 1 } { 2 x + 3 }$

B) $\frac { - 3 + x ^ { 2 } } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
C) $\frac { 3 - x ^ { 2 } } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
D) $\frac { 3 - x ^ { 2 } } { \left( x ^ { 2 } + 3 \right) }$
E) $\frac { 3 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$
F) $\frac { 1 } { 2 x }$
 
G) $\frac { 3 - x } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

H)None of these

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{x}{x^2 + 3}$ is found using the quotient rule: $\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{v \cdot u' - u \cdot v'}{v^2}$. Here, $u = x$ and $v = x^2 + 3$. Thus, $u' = 1$ and $v' = 2x$. Applying the quotient rule gives $\frac{(x^2 + 3) \cdot 1 - x \cdot 2x}{(x^2 + 3)^2} = \frac{3 - x^2}{(x^2 + 3)^2}$.

Find the Derivative Of f(x)=xx2+3f ( x ) = \frac { x } { x ^ { 2 } + 3 }f(x)=x2+3x​

Find the Derivative Of $f ( x ) = \frac { x } { x ^ { 2 } + 3 }$