y = f(x) 求:dy = ?dy = f'(x) dx举例:y = sin x + ln xdy = (cos x + 1/x) dx

微分dy,也就是导数的另一个写法 导数等同dy/dx

1 dy=-(1+cosx)/sin²xdx 2 dy=(sinx-xlnxcosx)/xsin²xdx 3 dy=sin2xdx 4 dy=e^x/cos²e^xdx

【3】y=x√(a²-x²)+a²arcsin(x/a)【a>0】dy=√(a²-x²)dx-[x²/√(a²-x²)]dx+[a/√(1-x²/a²)]dx=√(a²-x²)dx+[-x²/√(a²-x²)+a²/√(a²-x²)]dx=2√(a²-x²)dx

dy=(secxtanx^3+secx*2tanxsecx^2)dx=(secxtanx^3+2tanxsecx^3)dx

dy=sec[(e的x次方)]^2*d(e的x次方) dy=sec[(e的x次方)]^2*(e的x次方)dx

我觉得问题应该是问 dy / dx 的结果吧,e^y - x = xy 首先两边对x求导数,e^y * dy / dx - 1 = y + x * dy / dx (e^y - x) dy / dx = y + 1 dy / dx = (y + 1) / (e^y - x)

y'=sec²(x+y)*(1+y') y'[1-sec²(x+y)]=sec²(x+y) y'=sec²(x+y)/[1-sec²(x+y)] =-sec²(x+y)*cot²(x+y) =-1/sin²(x+y) 即dy/dx=-1/sin²(x+y) 所以dy=-dx/sin²(x+y)

先用两个函数乘积的求导公式,再用复合函数求导.

方程两边对x求导y+xy'+y'/y=0y'(x+1/y)=-yy'=-y/(x+1/y)=-y^2/(xy+1)所以dy=y'dx=-y^2/(xy+1)*dx