EEMajor12
Derivative of Integral (Drawing Pic now)
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EEMajor12
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f(x)=\int_{2x}^{3x^2} \tan x \, dt
EEMajor12
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|dw:1327887594561:dw|
Would it be -2\tan(2x)+6x \tan(3x^2)
myininaya
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having a little trouble reading
14yamaka
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try using the equations function below.
myininaya
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\[f(x)=\int\limits_{2x}^{3x^2}\tan(x) dx\]
myininaya
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is that right?
EEMajor12
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yes that is right myininaya
EEMajor12
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how will it take tex input?
\[-2\tan(2x)+6x \tan(3x^2)\]
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
\[f'(x)=(3x^2)'g(3x^2)-(2x)'g(2x)=6x g(3x^2)-2 g(2x)\]
\[=6x \cdot \tan(3x^2)-2 \cdot \tan(2x)\]
myininaya
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yes that is right! :)
EEMajor12
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Thank you! Got to love these forums!