Question

Differentiate (1) y = (1-x)(x² - 4)²

Answer 1

Given:

`y=(1-x)(x^2-4)^2`

Required:

To differentiate the given equation.

Step-by-step explanation:

Consider

`\begin{gathered} y=(1-x)(x^(2)-4)^(2) \\ \\ (dy)/(dx)=(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}`

Final Answer:

`(dy)/(dx)=-5x^4+4x^3+24x^2-16x-16`