Given:
[tex]y=(1-x)(x^2-4)^2[/tex]Required:
To differentiate the given equation.
Explanation:
Consider
[tex]\begin{gathered} y=(1-x)(x^{2}-4)^{2} \\ \\ \frac{dy}{dx}=\frac{d((1-x)(x^2-4)^2)}{dx} \\ \\ =(1-x)2(x^2-4)(2x)+(x^2-4)^2(-1) \\ \\ =4x(1-x)(x^2-4)-(x^2-4)^2 \\ \\ =4x(x^2-x^3-4+4x)-(x^4+16-8x^2) \\ \\ =4x^3-4x^4-16x+16x^2-x^4-16+8x^2 \\ \\ =-5x^4+4x^3+24x^2-16x-16 \end{gathered}[/tex]Final Answer:
[tex]\frac{dy}{dx}=-5x^4+4x^3+24x^2-16x-16[/tex]