To take the derivative of the given function, apply the power rule which is `(u*v)'=v*u'+u*v'` .
`u=1-4x-x^2` and `v=x^2-4`
Then, take the derivative of u and v to get u' and v'.
`u'=-4-2x` and `v'=2x`
And, plug-in u,v, u' and v' to the formula of product rule.
`f'(x)=(x^2-4)(-4-2x) + (1-4x-x^2)(2x)`
`f'(x)= -4x^2 -2x^3+16+8x+2x - 8x^2-2x^3`
Combine like terms.
`f'(x) = -4x^3-12x^2+10x+16`
Hence, the derivative of the given function is `f'(x)=-4x^3-12x^2+10x+16` .