Find the derivative of the function.
$$f ( x ) = \frac { 2 \sqrt { x } } { x ^ { 2 } + 9 }$$
A)
$\frac { - 3 x ^ { 2 } + 9 } { \sqrt { x } \left( x ^ { 2 } + 9 \right) ^ { 2 } }$
B)
$\frac { 1 } { 2 x \sqrt { x } \left( x ^ { 2 } + 9 \right) }$
C) $\frac { 1 } { 2 x \sqrt { x } }$
D) $\frac { - 3 x ^ { 2 } + 9 } { \sqrt { x } \left( x ^ { 2 } + 9 \right) }$

Question

Quizplus · Accepted Answer

Using the quotient rule, we have:$$f'(x) = \frac{(x^2+9)\frac{d}{dx}(2\sqrt{x}) - 2\sqrt{x}\frac{d}{dx}(x^2+9)}{(x^2+9)^2}$$$$= \frac{(x^2+9)\frac{1}{2\sqrt{x}} - 2\sqrt{x}(2x)}{(x^2+9)^2}$$$$= \frac{\frac{x^2+9}{2\sqrt{x}} - 4x\sqrt{x}}{(x^2+9)^2}$$$$= \frac{x^2+9 - 8x^2}{(x^2+9)^2\cdot 2\sqrt{x}}$$$$= \frac{-3x^2 + 9}{(x^2+9)^2\cdot 2\sqrt{x}}$$

Find the Derivative of the Function f(x)=2xx2+9f ( x ) = \frac { 2 \sqrt { x } } { x ^ { 2 } + 9 }f(x)=x2+92x​​

Find the Derivative of the Function $f ( x ) = \frac { 2 \sqrt { x } } { x ^ { 2 } + 9 }$