f(x)的导数为f'(x),且满足f(x)=3x^2+2xf'(2),求f'(5)

网友回答

∵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.
======以下答案可供参考======
供参考答案1:
f(x)=3x^2+2xf'(2)，f'(x)=6x+2f'(2)
则得f'(2)=12+2f'(2)
解得f'(2)=-12
则f'(x)=6x-24
则f'(5)=6×5-24＝6
则得f'(5)=6