Question

Did I do this problem correctly? (differentiation)

Answer 1

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

Answer 2

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

Answer 3

\(\huge \frac{-a+b}{a+b}\ne-1\)

Answer 4

@hartnn So is that all I can simplify?

Answer 5

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

Answer 6

Okay, Thanks @hartnn!

Answer 7

welcome ^_^