Formula sheet for Prelim 1 in Math 106 Differentiation formulas (xp)′= pxp-1(ex)′= ex(ln x)′= 1/x(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′Leibniz view of the chain rule: dfdfdgdxdgdx=⋅Equation of the tangent line to the graph at x0: 000()'()yfxfxxx=+−Algebra, Properties of e and ln: (a+b)2= a2+ 2ab + b2 1lim12.71828nnen→∞⎛⎞+==⎜⎟⎝⎠Definition. eln x =xln(ex) = x
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell University (Engineering School).