Chem452 HW - Chem 452 HW I(A) Winter 2011 ANSWERS for CHEM...

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Chem 452 – HW I(A) Winter 2011 ANSWERS for CHEM 452 HW 1(A) 1 2 9 x f(x) = cx n , df / dx = ncx n-1 , where c is a constant 2 () 4/3 1/3 1 3 x x a x a y = a x+y and f(x) = cx n , df / dx = ncx n-1 (c is a constant) 3 3ln( ) 3 x + () l n , 1 / f x x df dx x = = and d / dx (g(x)·h(x)) = ( d / dx g(x))(h(x)) + (g(x))( d / dx h(x)) 4 2 10 (1 ) x x ex + , ax ax f x e df dx ae == (where a is a constant) and d / dx (g(x)·h(x)) = ( d / dx g(x))(h(x)) + (g(x))( d / dx h(x)) 5 2 1 1 x 2 () ' ()' gx hxg x gxh x hx ⎛⎞ = ⎜⎟ ⎝⎠ (Quotient Rule) 6 1 x = (local min) x =− (local max) x = b ± b 2 4 ac 2 a Local min occurs at df / dx = 0 and d 2 f / dx 2 > 0 Local max occurs at df / dx = 0 and d 2 f / dx 2 < 0 7 12 [] 2 3 44 33 1 81 1 2 x x = += ax n dx = 1 n + 1 ( ) ax n + 1 for n 1 8 2 1 nRTln z z [ ] ( ) 2 2 1 1 21 ln ln ln ln z z z z nRT z nRT z z nRT = a x dx = a ln x
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