Question

How Solve it? Differentiate this function, thank you!

Answer 1

`(df)/(dx)=20x(4x^2-7x-8)(6x^2-7x-4)`

Explanation:

As we have to find derivative of a product of polynomials, we can use product rule here. It states that if `f(x)=g(x)h(x)k(x)`

then `(df)/(dx)=`

`(dg)/(dx)xxh(x)xxk(x)+(dh)/(dx)xxg(x)xxk(x)+(dk)/(dx)xxg(x)xxh(x)`

Here `f(x)=5x^2(4x^2-7x-8)^2`

= `5x^2(4x^2-7x-8)(4x^2-7x-8)`

Hence `(df)/(dx)=`

`5xx2x(4x^2-7x-8)(4x^2-7x-8)+(8x-7)xx5x^2(4x^2-7x-8)+(8x-7)xx5x^2(4x^2-7x-8)`

= `10x(4x^2-7x-8)^2+2xx5x^2(8x-7)(4x^2-7x-8)`

= `10x((4x^2-7x-8)^2+x(8x-7)(4x^2-7x-8))`

= `10x(4x^2-7x-8)((4x^2-7x-8)+x(8x-7))`

= `10x(4x^2-7x-8)(4x^2-7x-8+8x^2-7x)`

= `10x(4x^2-7x-8)(12x^2-14x-8)`

= `20x(4x^2-7x-8)(6x^2-7x-4)`