设f(x,y)有一阶连续偏导数,且f(x,x2)=1,f′x(x,x2)=x,求f′y(x,x2...答:f(x,x^2)=1 两边对x求导得:fx(x,x^2)+fy(x,x^2)2x=0 fy(x,x^2)=-fx(x,x^2)/(2x)=-1/2
高等数学多元微分题设f(x,y,z)=xy^2+yz^2+zx^2,求fxx(0,0,1) fxz(1...答:fzzx(x,y,z) =∂³f/∂z³=0 fxx(0,0,1)=2 fxz(1,0,2) = 2 fzzx(2,0,1) = 0 常用导数公式:1、y=c(c为常数) y'=0 2、y=x^n y'=nx^(n-1)3、y=a^x y'=a^xlna,y=e^x y'=e^x 4、y=logax y'=logae/x,y=lnx y'=1/x 5、...
设函数z=f(x,y),f对y的二阶偏导数=2,且f(x,0)=1,fy'(x,0)=x,求f(x...答:∵ f''y=2 ∴ f'y=2y+s(x)∵ f'y(x,0)=s(x)=x ∴ f'y=2y+x 从f(x,y)=y^2+xy+t(x)∵ f(x,0)=t(x)=1 ∴f(x,y)=y^2+xy+1