# QS418 - Math 217 Quiz Solutions 1(3 Points ex 1 ex Let u =...

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Math 217 Quiz Solutions 4/18/2013 1. (3 Points) R e x 1+ e x . Let u = e x + 1 so that du = e x dx . Substituting this, our integral becomes R 1 u du = ln( | u | ) + c = ln( e x + 1) + c . 2. (3 Points) d dx ( e sin( x ) ). We use the chain rule to determine the derivative is e sin( x ) cos( x ). In particular, it is the derivative of the outer function (the exponential) multiplied by the derivative of the inside function (the sine). 3. (4 Points) Prove that d dx a x = ln(