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Feb 13 lecture(xp)′= pxp-1(cf)′= cf′(f+g)′= f′+g′(fg)′= f′g + f g′(1/g)′= - g′/ g2(f/g)′= (f′g - f g′) / g2(f(g))′= f′(g) g′(ex)′= ex (eg)′= egg′Practice Problem.Find the derivative of 2xx efg = f′g + f g′(eg)′= egg′221/ 23/ 2()'21222xxxxx ex exexxxe−=⋅⎛⎞+⋅⎜⎟⎝⎠⎛⎞=+⎜⎟⎝⎠Bases other than e()()ln3ln3ln3( )3 Find '( )Recall ()''33'(ln3)(ln3)3xggxxxxxxf xfxee geee======Newton’s law of coolingAn object of temperature in a room of temperature ()(( ))((0))difference is reduced by 1/2 after time ln 2/ktTRdTk TRdtT tRTR ek−= −−−=−CSI-Ithaca0.0676A dead body in a 68room( )6830.6T te−=+DCoroner’s rule of thumb: cools 2 degrees in first hour and 1 degree per hour after that
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