f(x)=logaxf′(x)=__________f(x)=lnxf′(x)=__________3.几种常见函数的导数cosx-sinxaxlnaexnxn-104.导数的运算法则[f(x)±g(x)]′=______________________;[f(x)·g(x)]′=__________________________;[f(x)g(x)]′=____________________________[g(x)≠0].5.复合函数的求导法则f′[φ(x)]=____________或__________________.f′(x)±g′(x)f′(x)g(x)+g′(x)f(x)f′(u)φ′(x)y′x=y′u·u′x)C1.已知函数f(x)=4π2x2,则f′(x)=(A.4πx?B.8πxC.8π2x?D.16πx解析:函数f(x)=4π2x2的自变量为x,π为常量,所以f′(x)=8π2x.A解析:∵f′(x)=2ax,∴f′(1)=2a=2.∴a=1.2.已知函数f(x)=ax2+c,且f′(1)=2,则a的值为()A.1B.C.-1D.0)3.若f(x)在x0处可导,则f′(x0)等于(A的瞬时速度为_______,加速度为________.3-25.已知函数f(x)=xex,则f′(x)=________;函数f(x)的图象在点(0,f(0))处的切线方程为_______.(x+1)exy=x解析:∵f′(x)=ex+xex=(x+1)ex,∴f′(0)=1,f(0)=0,故函数f(x)的图象在点(0,f(0))处的切线方程为y=x.4.物体的运动方程是s=-t3+2t2-5,则物体在t=3时考点1导数的概念例1:设f(x)在x0处可导,下列式子中与f′(x0)相等的是()A.(1)(2)B.(1)(3)C.(2)(3)D.(1)(2)(3)(4)
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