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Study23
Did I do this problem correctly? (differentiation)
\(\ \huge \text{My steps:} \) \(\ \Huge f(x)=\frac{x}{(x^2+1)}.\) So to differentiate, I used the quotient rule: \(\ \Huge f'(x)=\frac{(1)(x^2+1)-(x)(2x)}{(x^2+1)^2}, \) \(\ \Huge = \frac{x^2+1-2x^2}{(x^2+1)^2}, \) \(\ \Huge = \frac{-x^2+1}{(x^2+1)^2}, \) \(\ \Huge = \frac{-\cancel{x^2+1}}{\cancel{(x^2+1)}^2}, \) \(\ \Huge = \frac{-1}{x^2+1} . \) \(\ \Huge \text{Is my work correct?} \)
\(\ \Huge = \frac{-x^2+1}{(x^2+1)^2}\) cannot be simplified further. you cannot cancel like that.
\(\huge \frac{-a+b}{a+b}\ne-1\)
@hartnn So is that all I can simplify?
yes, your final answer will be\( \Huge \frac{1-x^2}{(x^2+1)^2}\)