How Solve it? Differentiate this function, thank you!

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How Solve it? Differentiate this function, thank you!

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Answer 1 · 2017-03-15T16:36:09

$\frac{d f}{d x} = 20 x (4 x^{2} - 7 x - 8) (6 x^{2} - 7 x - 4)$ $(df)/(dx)=20x(4x^2-7x-8)(6x^2-7x-4)$

Explanation:

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

then $\frac{d f}{d x} =$ $(df)/(dx)=$

$\frac{d g}{d x} \times h (x) \times k (x) + \frac{d h}{d x} \times g (x) \times k (x) + \frac{d k}{d x} \times g (x) \times h (x)$ $(dg)/(dx)xxh(x)xxk(x)+(dh)/(dx)xxg(x)xxk(x)+(dk)/(dx)xxg(x)xxh(x)$

Here $f (x) = 5 x^{2} {(4 x^{2} - 7 x - 8)}^{2}$ $f(x)=5x^2(4x^2-7x-8)^2$

= $5 x^{2} (4 x^{2} - 7 x - 8) (4 x^{2} - 7 x - 8)$ $5x^2(4x^2-7x-8)(4x^2-7x-8)$

Hence $\frac{d f}{d x} =$ $(df)/(dx)=$

$5 \times 2 x (4 x^{2} - 7 x - 8) (4 x^{2} - 7 x - 8) + (8 x - 7) \times 5 x^{2} (4 x^{2} - 7 x - 8) + (8 x - 7) \times 5 x^{2} (4 x^{2} - 7 x - 8)$ $5xx2x(4x^2-7x-8)(4x^2-7x-8)+(8x-7)xx5x^2(4x^2-7x-8)+(8x-7)xx5x^2(4x^2-7x-8)$

= $10 x {(4 x^{2} - 7 x - 8)}^{2} + 2 \times 5 x^{2} (8 x - 7) (4 x^{2} - 7 x - 8)$ $10x(4x^2-7x-8)^2+2xx5x^2(8x-7)(4x^2-7x-8)$

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

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

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

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

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

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How Solve it? Differentiate this function, thank you!

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