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andrea723

  • 2 years ago

find the derivative f(x)=tan^(-1) (x/7)

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  1. No-data
    • 2 years ago
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    Do you know how to find the derivative of tan^(-1) ?

  2. andrea723
    • 2 years ago
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    1/x^2+1

  3. No-data
    • 2 years ago
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    let's use the chain rule.

  4. No-data
    • 2 years ago
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    \[y = \tan^{-1}(u)\]

  5. No-data
    • 2 years ago
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    \[u = \frac{x}{7}\]

  6. No-data
    • 2 years ago
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    we know that \[\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}\]

  7. No-data
    • 2 years ago
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    So \[\frac{dy}{dx}=\frac{1}{1+u^2}\frac{1}{7}\]

  8. No-data
    • 2 years ago
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    \[\frac{dy}{dx}=\frac{1}{1+(x/7)^2}\frac{1}{7}\]

  9. No-data
    • 2 years ago
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    Do you have any question?

  10. andrea723
    • 2 years ago
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    its that whole thing right? 1/1+(x/7)^2*1/7???

  11. No-data
    • 2 years ago
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    yes

  12. andrea723
    • 2 years ago
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    thank you

  13. No-data
    • 2 years ago
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    You're welcome.

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