其它极值点：f(π3,2π3)=−18 综上：f(x,y)∈[−18,1]画图如下：代码：x = 0 : 0.1 : pi; y = 0 : 0.1 : pi; [x, y] = meshgrid(x, y); z = cos(x).*cos(y).*cos(x-y); mesh(x, y, z); grid on; xlabel('x'); ylabel('y'); zlabel('z');不妨...
展开三角式 cos(x-y) cos(x−y)(x-y) 使用两角差的公式cos(x−y)=cos(x)cos(y)+sin(x)sin(y)cos(x-y)=cos(x)cos(y)+sin(x)sin(y)。 cos(x)cos(y)+sin(x)sin(y)cos(x)cos(y)+sin(x)sin(y)
函数表达式是 y=cos(x-y)?这样的话，对x求导过程就是:y'=-sin(x-y)*(1-y'),y'=y'*sin(x-y)-sin(x-y),y'*[sin(x-y)-1]=sin(x-y),y'=sin(x-y)/[sin(x-y)-1]
cos(x+y)cos(x−y) 評估 2cos(2x)+cos(2y) 對x 微分 −sin(2x) 測驗 Trigonometry cos(x+y)⋅cos(x−y)= 來自Web 搜索的類似問題 Finding the period of the solution toy′(x)=y(x)⋅cos(x+y(x))with Fourier transform; how to interpret complex result?
cos(x-y)=cosx*cosy+sinx*siny
x+y）=cosxcosy-sinxsiny 教材常用表达式有：（供参考）cos（α+β）=cosαcosβ-sinαsinβ cos（α-β）=cosαcosβ+sinαsinβ sin（α+β）=sinαcosβ+cosαsinβ sin（α-β）=sinαcosβ-cosαsinβ 这个公式的证明方法一般用解析法，如下：【因平方太多，写在几何画板上较方便】
-sin(xy)*(y+xy')=1-y'-ysin(xy)-xcos(xy)*y'=1-y'y'[1-xsin(xy)]=1+ysin(xy)y'=[1+ysin(xy)]/[1-xsin(xy)]也可用设二元函数f(x,y)=cos(xy)-x+y 用隐函数求导法:f'x(x,y)+f,y(x,y)*y'=0 f'x(x,y)=-sin(xy)*(xy)'-1 =-ysin(xy)-1 f'y(x,y...
令x+y=A,x-y=Bcos(x+y)cos(x-y)= cosAcosBx=(A+B)/2,y=(A-B)/2,代入cos^2(x)-sin^2(y)=cos2(A+B/2)-sin2(A-B/2)=[1+cos(A+B)-1+cos(A -B）]/2=cosAcosB-sinAsinB+cosAcosB+sinAsinB）/2=cosAcosB所以cos(x+y)cos(x-y)= cos2x-sin2y ...
dy/dx=-sin(xy)*(x*dy/dx+y)则：dy/dx(1+sin(xy)*x)=-sin(xy)*y 所以：dy/dx=(-sin(xy)*y)/(1+sin(xy)*x)
令u＝x－y,则y'＝1－u',原方程化为1－u'＝cosu,分离变量du/(1-cosu)＝dx,两边积分－cot(u/2)＝x＋C,代入u＝x－y,得－cot((x-y)/2)＝x＋C