y=sin(2x 5)的导数
来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 23:38:17
y=sin(e^-x)这是一个复合函数=cos(e^-x)*(e^-x)‘=-e^-x*cos(e^-x)
这是基本的三角变换公式,你可以去看看书里怎么写的
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
你算错了,导数分子是1,(cosx)′=-sinx;导数应是1/sin²x;
y=sin^3x是复合函数可以设t=sinxt'=cosxy=t^3y'=3t^2*t'y'=3sin^2x*cosx
y'={[(sinx)^n][(cosx)^n]}'=ncosx(sinx)^(n-1)-nsinx(cosx)^(n-1)
∵y=x^(sinx)∴lny=sinx*lnx两边求导:y'/y=cosx*lnx+(sinx)/x∴y'=y[cosx*lnx+(sinx)/x]=x^(sinx)[cosx*lnx+(sinx)
y=sin²2xy′=2×(cos2x)×2sin2x=4cos2x·sin2x=2sin4xy〃=2(4x)′cos4x=8cos4x
解析y=sinxsinxcosxy'=sinx'sinxcosx+sinx(sinxcosx)'=cosxsinx+sinx(sinx'cosx+sinxcosx')=cosxsinx+sinx(co
y‘=[sin²(cos3x)]'=2sin(cos3x)×[sin(cos(3x))]'=2sin(cos3x)cos(cos(3x))(cos3x)'=sin[2(cos3x)]×(-s
cosx谢谢o(︶︿︶)o再问:лл
2*cos(x^2)*x/sin(x)^2-2*sin(x^2)*cos(x)/sin(x)^3
y=sin(x^2)/(sinx)^2用对数求导简单:lny=lnsin(x^2)-ln(sinx)^2y'/y=2xcos(x^2)/sin(x^2)-2sinxcosx/(sinx)^2=2xco
y'=[2x(x+3)-x²]/(x+3)²=(x²+6x)/(x+3)²y'=cos(2x²+x)·(2x²+x)'=(4x+1)cos(
y'=6(sin3x)(cos3x)-5sinx^2(x^2)'=3sin6x-10xsinx^2
y=sin²x的n阶导数y'=2sinxcosx=sin2x;y''=2cos2x=2sin(π/2-2x);y'''=-4sin2x=4sin(π+2x);y⁽⁴&