f(x+y)=f(x)+f(y)+2xy lim f(h)/h =0 h 趋向0 问f'(x) 和f(x)
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/06 09:42:48
f(x+y)=f(x)+f(y)+2xy lim f(h)/h =0 h 趋向0 问f'(x) 和f(x)
f(x+y)=f(x)+f(y)+2xy lim f(h)/h =0 h 趋向0 问f'(x) 和f(x)
f(x+y)=f(x)+f(y)+2xy lim f(h)/h =0 h 趋向0 问f'(x) 和f(x)
f(x+y)=f(x)+f(y)+2xy,
移项,有f(x+y)-f(x) = f(y) + 2x
两边同除以y,有[f(x+y)- f(x)]/y = f(y)/y + 2x
也就是[f(x+y)- f(x)]/[(x+y)-x] = f(y)/y + 2x
对y→0取极限,有f'(x) = 0 + 2x
也就是f'(x) = 2x
于是f(x) = x²+C (其中C为常数)
代入f(x+y)=f(x)+f(y)+2xy验证,有C=0.
综上,f'(x) = 2x,f(x) = x².
f(x+y)=f(x)+f(y)+2xy
f(xy)=f(x)+f(y),证明f(x/y)=f(x)-f(y)
f(x+y)+f(xy-1)=f(x)f(y)+2f(n)表达式
f(xy,x-y)=x^2+y^2+xy;f(x,y)/∂x;f(x,y)/∂y
已知f(x+y)=f(x)+f(y)+2xy,求f(0)
f(x+y,x-y)=(x^2-y^2)/2xy,求f(x,y)!
f(x+y,x-y)=2xy(x-y),求f(x,y)
f(xy,x-y)=x^2+3xy+y^2,则f(x,y)=?
f(xy,x-y)=x^2-xy+y^2.求f(x,y)
y'=-2xy;求f(x).
f(xy)=f(x)+f(y),f(2)=1,f(3)=?
f(xy)=f(x)+f(y)且f(8)=3则f(2)=
f(xy)=f(x)+f(y),f(8)=3,则f(根2)等于
f(xy)=f(x)+f(y),f(8)=3,求f(√2),
f'(0)=1,f(x+y)=f(x)+f(y)+2xy,求f(x)
f(x)满足f(x+y)+f(xy)=2f(x)f(y)求函数的奇偶性
导数:f(x+y)=f(x)f(y),且f'(o)=1,求f'(x)f(x+y)=f(x)f(y),且f'(o)=1,求f'(x)f(x+y)=f(x)+f(y)+2xy,且f'(o)存在,求f'(x) f(1+x)=af(x),且f'(0)=b,求f'(1)
设f(x+y,x-y)=x^2+xy,求f(x,y)