$\text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } } { 1 + x ^ { 2 } } \text {. Simplify your answer. }$
A) $\frac { - e ^ { x } \left( x ^ { 2 } - 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$
B)$\frac { e ^ { x } \left( x ^ { 2 } - 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) }$
C)$\frac { e ^ { x } \left( x ^ { 2 } - 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$
D)$\frac { e ^ { x } \left( x ^ { 2 } + 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$
E) $\frac { e ^ { x } } { 2 x }$

Question

$\text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } } { 1 + x ^ { 2 } } \text {. Simplify your answer. }$ 
A) $\frac { - e ^ { x } \left( x ^ { 2 } - 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$
B)$\frac { e ^ { x } \left( x ^ { 2 } - 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) }$
C)$\frac { e ^ { x } \left( x ^ { 2 } - 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$
D)$\frac { e ^ { x } \left( x ^ { 2 } + 2 x + 1 \right) } { \left( 1 + x ^ { 2 } \right) ^ { 2 } }$
E) $\frac { e ^ { x } } { 2 x }$

Quizplus · Accepted Answer

We can apply quotient rule to find the derivative of the given function.
$$f(x)=\frac{e^x}{1+x^2}$$
$$f'(x)=\frac{(1+x^2)\frac{d}{dx}(e^x)-e^x\frac{d}{dx}(1+x^2)}{(1+x^2)^2}$$
$$=\frac{(1+x^2)e^x-e^x(2x)}{(1+x^2)^2}$$
$$=\frac{e^x(x^2-2x+1)}{(1+x^2)^2}$$
Thus, the correct choice is (C).

Find the derivative of the function f(x)=ex1+x2. Simplify your answer. \text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } } { 1 + x ^ { 2 } } \text {. Simplify your answer. } Find the derivative of the function f(x)=1+x2ex​. Simplify your answer.

$\text { Find the derivative of the function } f ( x ) = \frac { e ^ { x } } { 1 + x ^ { 2 } } \text {. Simplify your answer. }$