## Study23 Group Title Did I do this problem correctly? (differentiation) one year ago one year ago

1. Study23 Group Title

$$\ \huge \text{My steps:}$$ $$\ \Huge f(x)=\frac{x}{(x^2+1)}.$$ So to differentiate, I used the quotient rule: $$\ \Huge f'(x)=\frac{(1)(x^2+1)-(x)(2x)}{(x^2+1)^2},$$ $$\ \Huge = \frac{x^2+1-2x^2}{(x^2+1)^2},$$ $$\ \Huge = \frac{-x^2+1}{(x^2+1)^2},$$ $$\ \Huge = \frac{-\cancel{x^2+1}}{\cancel{(x^2+1)}^2},$$ $$\ \Huge = \frac{-1}{x^2+1} .$$ $$\ \Huge \text{Is my work correct?}$$

2. hartnn Group Title

$$\ \Huge = \frac{-x^2+1}{(x^2+1)^2}$$ cannot be simplified further. you cannot cancel like that.

3. hartnn Group Title

$$\huge \frac{-a+b}{a+b}\ne-1$$

4. Study23 Group Title

@hartnn So is that all I can simplify?

5. hartnn Group Title

yes, your final answer will be$$\Huge \frac{1-x^2}{(x^2+1)^2}$$

6. Study23 Group Title

Okay, Thanks @hartnn!

7. hartnn Group Title

welcome ^_^