For x > 0, define

Calculate

and

y''(x) :=

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- Feb 21st 2011, 05:11 AMmaximus101find y'(x) and y''(x) when y is defined with an integral
For x > 0, define

Calculate

and

y''(x) := - Feb 21st 2011, 05:13 AMAckbeet
You'll need the Leibniz Rule, the product rule, and the chain rule to differentiate your y(x). What do you get?

- Feb 21st 2011, 06:38 AMHallsofIvy
Since there is no x inside the integral, strictly speaking you don't need the full "Leibniz rule", just the "Fundamental theorem of Calculus" and the chain rule.

- Feb 21st 2011, 08:01 AMtom@ballooncalculus
Just in case a picture helps...

http://www.ballooncalculus.org/draw/ftc/two.png

... where (key in spoiler) ...

__Spoiler__:

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

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