高二数学选修2-2导数12种题型归纳(中等难度)汇编

导数题型分类解析（中等难度）yf(xx)f(x)yf(x)xf'(x)lim=lim在x到x+=00xΔx0000x0x0yf(x)在x00f(xh)f(xh)yf(x)(a,b)x(a,b)lim例则）000hh0f(x)2f(x)2f(x)A．'．．D．0''000f(xh)f(xh)f(x)3lim例'（）00h0h0369．．．f(xh)f(x)2例lim00hh0f'(x)f(x)x将000f2fxx3xf2例2fxfxxf例.44f(x)f(x)2f(2x)x8x8yf(x)f)例在R2）y2x1yxy3x2y2x3tt例s1tt2st3例st）ssssOtOtOtOt．．C．．①CC②xnnxn1;③⑦xx;④xx;11lnx(e)e;(a)alnalogxloge⑤⑥;;⑧.xxxxxxaa例()1111log33excosx2xsinx．x．x=．D．xx22x2xx23xsinx,fxfx,fxfx,，fxfx,nN例fx0f1021n1n(Cu)Cu.uv)uv.''('''uu'vuv'(uv)uvuv.'''vv2例logxe21xyx3xn2(()*()fxfx1(1cos2x)3ysin2例）y）x3例x4()°°°°,yx1xxa,则nna1nS.nn例yx2P3).例y2xx3.(x)=x+x-2py=4x-1p例f在）300．．(1,和(1,和．．例yx4lx4y80l）4xy30x4y504xy30．x4y30．．D．lnx(x)例f.xlx(x)lnxax(2a)x()fx例f2x(x)xaxb(a,bR)()fx例f32x例fxyfx.(x)3x2x1m,0例f32m.mxxxmR例fxfxm323.21fxxx1aRfx,例332a33围.11(x)x(2a)x(1a)x(a0).f(x)例4f若在[0，1]a3232围.(x)x3ax例f在R上有两个极值点，则实数a.2fxxalnxgxfx2在a例x112m2x2n8x1mn0例fx22（））22例.3.例=x2e.x例fx./()fx例）））））1yx34x1例()3yyyy642o24xo24xy24xoxyf(x)在(a,b)f(x)(a,b)内例的图bf(x)(a,b)Oax为.f(x)f(x)yf(x)的例y((x))例(有11)有22有31有13例()＜＜＜＜ff(2)f(2)ff(2)＜＜＜f(2)fπ(sinxcosx)dx例：）2π2π44(x)e|x|f(x)例f21[1(xx例2）0π2ππ1π114242例==3）1117124312x4x3B例y2例1PP）11114567sinx(0xπ)例π2y与x）12π3ππ4π练习题f(xx)f(x)1f'(x)）00x0x012122f4(x)x2xf'6f'2）02练：已知，是的导函数，即，，fxfxfxsinxcosxfxfx1n1n21fxfxnN，则f，x________.n1n2014(x)lnxaxf（）π[0,]42P=xCPP）13]2[][[21(x)x24x3lnxft2a(x)axa)x3ax(