函数f(x)的导数为f′(x),且满足f(x)=3x^2+2xf′(2),则f′(5)=--------?

问题描述:

函数f(x)的导数为f′(x),且满足f(x)=3x^2+2xf′(2),则f′(5)=--------?

∵f(x)=3x^2+2xf'(2),
∴f'(x)=6x+2f'(2),
∴f'(2)=12+2f'(2),
即f'(2)=-12.
∴f(x)=3x^2-24x,
∴f'(x)=6x-24,
故f'(5)=6.