anonymous
  • anonymous
Derivative of Integral (Drawing Pic now)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
f(x)=\int_{2x}^{3x^2} \tan x \, dt
anonymous
  • anonymous
|dw:1327887594561:dw| Would it be -2\tan(2x)+6x \tan(3x^2)
myininaya
  • myininaya
having a little trouble reading

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anonymous
  • anonymous
try using the equations function below.
myininaya
  • myininaya
\[f(x)=\int\limits_{2x}^{3x^2}\tan(x) dx\]
myininaya
  • myininaya
is that right?
anonymous
  • anonymous
yes that is right myininaya
anonymous
  • anonymous
how will it take tex input? \[-2\tan(2x)+6x \tan(3x^2)\]
myininaya
  • myininaya
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 \[f'(x)=(3x^2)'g(3x^2)-(2x)'g(2x)=6x g(3x^2)-2 g(2x)\] \[=6x \cdot \tan(3x^2)-2 \cdot \tan(2x)\]
myininaya
  • myininaya
yes that is right! :)
anonymous
  • anonymous
Thank you! Got to love these forums!

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