Question

Find the derivative using the Power Rule and the Product Rule.Y=(-2x^4-3)(-2x^2+1)

Answer 1

Given the function:

`y=(-2x^4-3)(-2x^2+1)`
`\begin{gathered} \text{let u=-2x}^4-3 \\ (du)/(dx)=-8x^3-0=-8x^3 \\ \\ \text{let v=-2x}^2+1 \\ (dv)/(dx)=-4x+0=-4x \end{gathered}`

By applying the product rule, we have:

`y^{^(\prime)}=V(du)/(dx)+U(dv)/(dx)`

Thus, we have:

`\begin{gathered} y^{^(\prime)}=(-2x^2+1)(-8x^3)+(-2x^4-3)(-4x) \\ y^{^(\prime)}=16x^5-8x^3+8x^5+12x \\ y^{^(\prime)}=16x^5+8x^5-8x^3+12x \\ y^{^(\prime)}=24x^5-8x^3+12x \end{gathered}`