anonymous
  • anonymous
find F'(x) when F(x)= integral from 4 to x^2 (2 sqrt(1+t^3) dt)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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freckles
  • freckles
\[F(x)=\int\limits_4^{x^2} g(t) dt=G(t)|_4^{x^2}=G(x^2)-G(4) \\ \text{so we have } F(x)=G(x^2)-G(4) \\ \text{ differentiate both sides }\]
freckles
  • freckles
\[F'(x)=(x^2)'g(x^2)-0 \text{ by chain rule and constant rule }\]
freckles
  • freckles
@aawowaa are you there?

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IrishBoy123
  • IrishBoy123
+
anonymous
  • anonymous
yes, I'm going over it.
freckles
  • freckles
you understand that g(t) is 2sqrt(1+t^3)
freckles
  • freckles
And that I was using G(t) to represent the antiderivative of g(t) that is G'=g
anonymous
  • anonymous
yes, I understand
anonymous
  • anonymous
so now I plug in 2sqrt(1+t^3) back?
freckles
  • freckles
g(t)=2sqrt(1+t^3) so g(x^2)=?"
anonymous
  • anonymous
=2sqrt(1+x^6)
freckles
  • freckles
ok so that is what you replace g(x^2) with
freckles
  • freckles
don't forget to find (x^2)' which is next to g(x^2)
anonymous
  • anonymous
thank you I got it
freckles
  • freckles
np

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