设函数y=y(x)由方程y=f(x^2+y^2)+f(x+y)确定,且y(0)=2,f(x)是可导函数,f'(2)=1/2,f'(4)=1,则f'(0)的值

设函数y=y(x)由方程y=f(x^2+y^2)+f(x+y)确定,且y(0)=2,f(x)是可导函数,f'(2)=1/2,f'(4)=1,则f'(0)的值
设函数y=y(x)由方程y=f(x^2+y^2)+f(x+y)确定,且y(0)=2,f(x)是可导函数,f'(2)=1/2,f'(4)=1,则f'(0)的值

设函数y=y(x)由方程y=f(x^2+y^2)+f(x+y)确定,且y(0)=2,f(x)是可导函数,f'(2)=1/2,f'(4)=1,则f'(0)的值
y=f(x²+y²)+f(x+y)
y'=f'(x²+y²)×(x²+y²)'+f'(x+y)×(x+y)'
=(2x+2yy')f'(x²+y²)+(1+y')f'(x+y)
当x=0时,y=2,那么y'=(0+4y')f'(4)+(1+y')f'(2)
而f'(4)=1,f'(2)=1/2,所以y'=4y'×1+(1+y')×(1/2)
即：y'=4y'+1/2+y'/2,所以y'=-1/7,即f'(0)=-1/7