若F(x)=f(3f(4f(x))),f(0)=0,f'(0)=2,求F'(0)如题
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![若F(x)=f(3f(4f(x))),f(0)=0,f'(0)=2,求F'(0)如题](/uploads/image/z/12540349-37-9.jpg?t=%E8%8B%A5F%28x%29%3Df%283f%284f%28x%29%29%29%2Cf%280%29%3D0%2Cf%27%280%29%3D2%2C%E6%B1%82F%27%280%29%E5%A6%82%E9%A2%98)
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.