20xxap微積分calculus知識(shí)點(diǎn)總結(jié)(已修改)
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【正文】 吳靜彬 編寫 1 CALCULUS A DERIVATIVE FUNCTION 1. The derivative function or simply the derivative is defined as )(xf? ＝ y? ＝ x xfxxfxy xx ? ?????? ???? )()(limlim 00 2. Find the derivative function a) Find y? , b) Find the average rate of change xy?? , c) Find the limit xyx ???? 0lim. 3. Geometric significance Consider a general function y=f(x), a fixed point A(a,f(a)) and a variable point B(x,f(x)). The slope of chord AB= ax afxf ?? )()( . Now as B? A, x? a and the slope of chord AB ? slope of tangent at A. So, ax afxfax ???)()(lim is )(af? . Thus, we can know the derivative at x=a is the slope of the tangent at x=a. 吳靜彬 編寫 2 4. Rules )(xf )(xf? C(a constant) 0 nx 1?nnx xsin xcos xcos xsin? xtan xx22 co s1sec
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