arctan(y x)=ln(根号下x2 y2)
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两边对【x】求导,注意,y是x的函数,利用复合函数求导1/[1+(y/x)^2]×(y/x)'=1/2×1/(x^2+y^2)×(x^2+y^2)',也就是:x^2/(x^2+y^2)×(xy'-y)
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y=arctan(a/x)+1/2[ln(x-a)-ln(x+a)],利用复合函数求导的链锁规则,有y'=1/(1+(a/x)^2)*(-a/x^2)+1/2[1/(x-a)]-1/(x+a)]=-a
dy/dx=(y-2x)/(2y-x),要详解吗?再问:���д
两边同时对x求导,得(2x+2yy')/(x²+y²)=1/(1+y²/x²)·(xy'-y)/x²(2x+2yy')/(x²+y²
tan[arctan(-2)+arctan(-3)]=-2-3/1-6(用余切公式)=1所以arctan(-2)+arctan(-3)=45度或225度
两边同时求导根据链式法则1/2(x²+y²)’/(x²+y²)=(x/y)'/[1+(x/y)²]1/2(2x+2yy')/(x²+y
直接写重要步骤:两端对x求导,化简,得y-y'x=2x+2y-y'y'=(y-2x)/(x+2y)两端再对x求导,化简,并将上一步结果代入,得y''=-10(x^2+y^2)/(x+2y)^3
两边求导(y'x-y/x^2)/[1+(y/x)^2]=x+yy'/(x^2+y^2)^1/2整理y'x-y=(x+yy')(x^2+y^2)^1/2
注意到当n趋于无穷时,lnn/n的极限是0,因此|lnn*sinn|0.5n,趋于正无穷,于是arctan(n--lnn*sinn)趋于pi/2.再问:为什么|lnn*sinn|
y=f{g[h(p(x))]}y'=f'(g)g'(h)h'(p)p'(x)y'=1/cos(arctan(sinx))*(-sin(arctan(sinx))*cosx/(1+sinx^2)=-ta
对x求导1/√(x²+y²)*[1/2√(x²+y²)]*(2x+2y*y')=1/(1+y²/x²)]*(y'*x-y)/x²(
对x求导0.5*1/(x²+y²)*(x²+y²)'=1/[1+(y/x)²]*(y/x)'0.5/(x²+y²)*(2x+2y*
即0.5ln(x^2+y^2)=arctan(y/x)对x求导得到0.5(2x+2y*y')/(x^2+y^2)=1/(1+y^2/x^2)*(y/x)'即(2x+2y*y')/(x^2+y^2)=2
原式化简为1/2ln(x^2+y^2)=arctany/x两边对x求导,得1/2×1/(x^2+y^2)×(2x+2yy')=1/[1+(y/x)^2]×(y'x-y)/x^2化简得y'=(x+y)/
即(10x+y)*(10y+x)=2268101xy+10x²+10y²=2268因为后面的10x²+10y²只可能是整十的数,所以2268中的个位8要靠101