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2.1 Class Notes

# 2.1 Class Notes - Feb 13 lecture Practice Problem Find the...

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Feb 13 lecture (x p ) = px p-1 (cf) = cf (f+g) = f +g (fg) = f g + f g (1/g) = - g / g 2 (f/g) = (f g - f g ) / g 2 (f(g)) = f (g) g (e x ) = e x (e g ) = e g g Practice Problem. Find the derivative of 2 x x e fg = f g + f g (e g ) = e g g 2 2 1/ 2 3/ 2 ( )' 2 1 2 2 2 x x x x x e x e x e x x x e = + = + Bases other than e ( ) ( ) ln3 ln3 ln3 ( ) 3 Find '( ) Recall ( )' ' 3 3 ' (ln3) (ln3)3 x g g x x x x x x f x f x e e g e e e = = = = = = Newton’s law of cooling An object of temperature in a room of temperature ( ) ( ( ) ) ( (0) ) difference is reduced by 1/2 after time ln 2/ kt T R dT k T R dt T t R T R e k = − = CSI-Ithaca 0.0676 A dead body in a 68 room ( ) 68 30.6 T t e = + D Coroner’s rule of thumb: cools 2 degrees in first hour and 1 degree per hour after that

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