求arctan((x y) 1-xy)的二阶偏导数-搜答案-智慧作业帮

arctan√(x+1)的定义域:x+1>=0x>=-1值域:(kπ,kπ+π/2),k为整数

步骤如下:

dz/dx=arctan(xy)+xy/[1+(xy)^2](dz/dx)|(1,1)=π/4+1/2(dz/dy)|(1,1)=x^2/[1+(xy)^2]=1/2

我尽力做,你自己验算下吧

z=arctan(x*e^x)z'={1/[1+(x*e^x)^2]}*(x*e^x)'(x*e^x)'=x'*e^x+x*(e^x)'=e^x+x*e^x=(x+1)*e^x所以dz/dx=(x+1

y=arctan(1-x)1-x=tany对x求导-1=y'sec²y所以y'=-1/sec²y=-cos²y=-cos²[arctan(1-x)]y'=-co

arctanx'=1/(1+x^2)y=arctan(x+1)^1/2y'=1/(1+(x+1)^1/2^2)*(x+1)^1/2'y'=1/(x+2)*1/2(x+1)^(-1/2)y'=1/[2(

令t=1/x原式=∫(arctant)/(1+1/t^2)d(1/t)=-∫(arctant)/(t^2+1)dt=-∫arctantdarctant=-1/2(arctant)^2+C=-1/2(a

设x=sect原式=∫tdsect=tsect-∫sectdt=tsect-ln|sect+tant|+C=xarccos(1/x)-ln|x+√(x^2-1)|+C

令1/x=t则原式=∫arctant/(1+1/t²)*(-1/t²)dt=∫-arctant/(1+t²)dt=∫-arctantdarctant=-1/2arctan

嘿嘿,其实这题很简单.令y=1/x、x=1/y、dx=-1/y²dy∫[arctan(1/x)]/(1+x²)dx=∫arctany/(1+1/y²)*(-1/y

此题先分部积分,然后关键是求一个有理式的积分,用配对积分法求出会相对简单很多.做出来了,但式子实在太繁琐,你要的话,我可以QQ发给你178614247 给分吧!哈哈

因为x=（x^1/2)^2那么dx=2d（x^1/2)所以原式=2arctan（x^1/2)d(x^1/2)=2/[1+(x^1/2)^2

dy/dx=1/[1+(1+x^2)]*2x刚考过导数表示非常苦逼.哎我还是讲清楚点这是复合函数,把它拆成y=arctanuu=1+x^2再分别求导数再问：·再答：==dy/dx=[arctan(1+

分部积分：∫arctan(1/x)dx=arctan(1/x)*x-∫x*1/(1+1/x^2)*(-1/x^2)dx=arctan(1/x)*x+∫x*1/(1+x^2)dx=arctan(1/x)

须知(e^x)'=e^x,(arctanx)'=1/(1+x²)y=e^arctan(1/x)y'=e^arctan(1/x)·1/[1+(1/x)²]·(-1/x²)=

tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(arctan(1-x)+arctan(1+x))=(1-x+1+x)/(1-(1-x)(1+x))=2/x^2arctan(1

左右2边取正切,左边=(X+Y)/(1-XY)=右边.左边=arctan[(X+Y)/(1-XY)+Z]/[1-(X+Y)Z/(1-XY)]=arctanc(X+Y+Z-XYZ)/[1-XY-(X+Y

y=arctan(1-x/1+x),求dy

此题复合求导dy=d[arctan(1-x/1+x)]=[1/(1+(1-x/1+x)^2)]·(1-x/1+x)';注：(arctanx)'=1/(1+x^2)=-(1/(x^2+1))