若F(x)=f(3f(4f(x))),f(0)=0,f'(0)=2,求F'(0)如题

若F(x)=f(3f(4f(x))),f(0)=0,f'(0)=2,求F'(0)如题
若F(x)=f(3f(4f(x))),f(0)=0,f'(0)=2,求F'(0)
如题

若F(x)=f(3f(4f(x))),f(0)=0,f'(0)=2,求F'(0)如题
复合求导:
F'(x)=f'(3f(4f(x)))3f'(4f(x)))4f'(x)
F'(0)=2*3*2*4*2=96

F(x)=f(3f(4f(x)))
∴
F'(x)
=f'(3f(4f(x)))*3*[f(4f(x))]'
=3f'(3f(4f(x)))*f'(4f(x))*4*f'(x)
=12f'(3f(4f(x)))*f'(4f(x))*f'(x)
故
F'(0)
=12f'(3f(4f(0)))*f'(4f(0))*f'(0)
=12f'(0)*f'(0)*f'(0)
=12*2^3
=12*8
=96.