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EEMajor12

Derivative of Integral (Drawing Pic now)

  • 2 years ago
  • 2 years ago

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  1. EEMajor12
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    f(x)=\int_{2x}^{3x^2} \tan x \, dt

    • 2 years ago
  2. EEMajor12
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    |dw:1327887594561:dw| Would it be -2\tan(2x)+6x \tan(3x^2)

    • 2 years ago
  3. myininaya
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    having a little trouble reading

    • 2 years ago
  4. 14yamaka
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    try using the equations function below.

    • 2 years ago
  5. myininaya
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    \[f(x)=\int\limits_{2x}^{3x^2}\tan(x) dx\]

    • 2 years ago
  6. myininaya
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    is that right?

    • 2 years ago
  7. EEMajor12
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    yes that is right myininaya

    • 2 years ago
  8. EEMajor12
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    how will it take tex input? \[-2\tan(2x)+6x \tan(3x^2)\]

    • 2 years ago
  9. myininaya
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    Let g(x)=tan(x) and let G be the antiderivative of g so we have \[f(x)=G(x)|_{2x}^{3x^2}=G(3x^2)-G(2x)\] so \[f'(x)=(3x^2)'g(3x^2)-(2x)'g(2x)=6x g(3x^2)-2 g(2x)\] \[=6x \cdot \tan(3x^2)-2 \cdot \tan(2x)\]

    • 2 years ago
  10. myininaya
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    yes that is right! :)

    • 2 years ago
  11. EEMajor12
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    Thank you! Got to love these forums!

    • 2 years ago
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