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Study23

  • 3 years ago

Did I do this problem correctly? (differentiation)

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  1. Study23
    • 3 years ago
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    \(\ \huge \text{My steps:} \) \(\ \Huge f(x)=\frac{x}{(x^2+1)}.\) 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
    • 3 years ago
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    \(\ \Huge = \frac{-x^2+1}{(x^2+1)^2}\) cannot be simplified further. you cannot cancel like that.

  3. hartnn
    • 3 years ago
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    \(\huge \frac{-a+b}{a+b}\ne-1\)

  4. Study23
    • 3 years ago
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    @hartnn So is that all I can simplify?

  5. hartnn
    • 3 years ago
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    yes, your final answer will be\( \Huge \frac{1-x^2}{(x^2+1)^2}\)

  6. Study23
    • 3 years ago
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    Okay, Thanks @hartnn!

  7. hartnn
    • 3 years ago
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    welcome ^_^

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