My Math Forum find y'(x) and y''(x) when y is defined with an integral

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 February 21st, 2011, 05:03 AM #1 Member   Joined: Feb 2011 Posts: 58 Thanks: 0 find y'(x) and y''(x) when y is defined with an integral For x > 0, define $y(x) := x$ $\int_0^{log x} \! sqrt{1 + e^t} dt -(2/3)(1 + x)^{3/2} \$ Calculate $y'(x) := dy/dx$ and y''(x) := $d^2y/dx^2$
 February 21st, 2011, 06:31 AM #2 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 Re: find y'(x) and y''(x) when y is defined with an integral For the first derivative, you need to use the product rule. The second factor in the first term will require the fundamental theorem of calculus (substitute logx for t) and the chain rule (differentiate log x). The second term is straightforward. Show your attempt at the problem and we'll let you know if there are any errors.

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