What is the derivative of (x^3-4x)(2x^2+5x) ?

The derivative of (x^3-4x)(2x^2+5x) is 10x^4+20x^3-24x^2-40x

What is the first derivative of (x^3-4x)(2x^2+5x) ?

The first derivative of (x^3-4x)(2x^2+5x) is 10x^4+20x^3-24x^2-40x

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derivative of

(x^{3} - 4 x) (2 x^{2} + 5 x)

10 x^{4} + 20 x^{3} - 24 x^{2} - 40 x

Solution steps

\frac{d}{d x} ((x^{3} - 4 x) (2 x^{2} + 5 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3} - 4 x, g = 2 x^{2} + 5 x

= \frac{d}{d x} (x^{3} - 4 x) (2 x^{2} + 5 x) + \frac{d}{d x} (2 x^{2} + 5 x) (x^{3} - 4 x)

\frac{d}{d x} (x^{3} - 4 x) = 3 x^{2} - 4

\frac{d}{d x} (2 x^{2} + 5 x) = 4 x + 5

= (3 x^{2} - 4) (2 x^{2} + 5 x) + (4 x + 5) (x^{3} - 4 x)

Simplify

(3 x^{2} - 4) (2 x^{2} + 5 x) + (4 x + 5) (x^{3} - 4 x) : 10 x^{4} + 20 x^{3} - 24 x^{2} - 40 x

= 10 x^{4} + 20 x^{3} - 24 x^{2} - 40 x

What is the derivative of (x^3-4x)(2x^2+5x) ?
The derivative of (x^3-4x)(2x^2+5x) is 10x^4+20x^3-24x^2-40x
What is the first derivative of (x^3-4x)(2x^2+5x) ?
The first derivative of (x^3-4x)(2x^2+5x) is 10x^4+20x^3-24x^2-40x