百度作业网求y=3sin(2x 3)的导数
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 13:57:37
y=sin（e^-x）这是一个复合函数＝cos（e^-x）*（e^-x）‘＝-e^-x*cos（e^-x）
本题考查的是函数的求导原则,总共有三大类：①f(x)±g(x)②f(x)*g(x)③f(x)/g(x)
y=sin³xy'=(3sin²x)×(sinx)'y'=3cosxsin²x
两边求导：cos(x+y)*(1+y')=cosx+cosy*y'y'=(cosx-cos(x+y))/(cos(x+y)-cosy)e^x+1=e^y*y'+y'y'=(e^x+1)/(e^y+1)
y'=2sinx*cosx-sinx²*2x=sin2x-2xsinx²
y=sin^nxcos^nxy′=nsin^(n-1)xcosxcos^nx+ncos^(n-1)x(-sinx)sin^nx=nsin^(n-1)xcos^(n-1)x(cos²x-sin
先对ln求导,得1/sin(1+3x^2)然后对真数,即sin(1+3x^2)求导,是cos(1+3x^2)然后对1+3x^2求导,是6x最后相乘y'=6xcos(1+3x^2)/sin(1+3x^2
y=sin^3x是复合函数可以设t=sinxt'=cosxy=t^3y'=3t^2*t'y'=3sin^2x*cosx
∵y=cosx*sin(3x+2)∴y'=(cosx)'*sin(3x+2)+cosx*[sin(3x+2)]'=-sinx*sin(3x+2)+cosx*3cos(3x+2)=3cosxcos(3x
由题意,得斜率=3×1平方=3所以切线方程为y-1=3(x-1)即y=3x-2
y＝sin³x-sin3x→y'＝3sinx·(sinx)'-cos3x·(3x)'→y'＝3sin²xcosx-3cosx→y'＝3(1-cos²x)cosx-3cos
y=sin²2xy′=2×(cos2x)×2sin2x=4cos2x·sin2x=2sin4xy〃=2(4x)′cos4x=8cos4x
y＝2sin²(2x+π/3)＝1-cos(4x+2π/3).∴y'＝sin(4x+2π/3)·(4x+2π/3)'＝4sin(4x+2π/3).
y‘=[sin²(cos3x)]'=2sin(cos3x)×[sin(cos(3x))]'=2sin(cos3x)cos(cos(3x))(cos3x)'=sin[2(cos3x)]×(-s
2*cos(x^2)*x/sin(x)^2-2*sin(x^2)*cos(x)/sin(x)^3
y=[sin(4x+3)]^3y'=3[sin(4x+3)]^2*[sin(4x+3)]'=3[sin(4x+3)]^2*[cos(4x+3)]*(4x+3)'=12[sin(4x+3)]^2*[co
y是2次复合y=u^2u=sinvv=3x+π/4y'=2u*u'*v'∴y'=2sin(3x+π/4)*cos(3x+π/4)*(3x+π/4)'=2sin(3x+π/4)*cos(3x+π/4)*