How Solve it? Differentiate this function, thank you!

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Answer 1 · 2017-03-15T16:36:09

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

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 $(df)/(dx)=$

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

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

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

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

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

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

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