What is the derivative of (x^3-12x)(3x^2+2x) ?

The derivative of (x^3-12x)(3x^2+2x) is 15x^4+8x^3-108x^2-48x

What is the first derivative of (x^3-12x)(3x^2+2x) ?

The first derivative of (x^3-12x)(3x^2+2x) is 15x^4+8x^3-108x^2-48x

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derivative of

(x^{3} - 12 x) (3 x^{2} + 2 x)

15 x^{4} + 8 x^{3} - 108 x^{2} - 48 x

Solution steps

\frac{d}{d x} ((x^{3} - 12 x) (3 x^{2} + 2 x))

Apply the Product Rule:

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

f = x^{3} - 12 x, g = 3 x^{2} + 2 x

= \frac{d}{d x} (x^{3} - 12 x) (3 x^{2} + 2 x) + \frac{d}{d x} (3 x^{2} + 2 x) (x^{3} - 12 x)

\frac{d}{d x} (x^{3} - 12 x) = 3 x^{2} - 12

\frac{d}{d x} (3 x^{2} + 2 x) = 6 x + 2

= (3 x^{2} - 12) (3 x^{2} + 2 x) + (6 x + 2) (x^{3} - 12 x)

Simplify

(3 x^{2} - 12) (3 x^{2} + 2 x) + (6 x + 2) (x^{3} - 12 x) : 15 x^{4} + 8 x^{3} - 108 x^{2} - 48 x

= 15 x^{4} + 8 x^{3} - 108 x^{2} - 48 x

\frac{d}{d x} ((2^{x} \cdot x^{- 2})^{3 x - 1})

(3 x e^{x})^{^{'}}

\int x \frac{d}{1} (y) d x

\frac{\partial}{\partial x} (x \cdot ln (x + 2 y) + \frac{x}{y})

x \to 3 - lim (\frac{x - 3}{∣ x - 3 ∣})

What is the derivative of (x^3-12x)(3x^2+2x) ?
The derivative of (x^3-12x)(3x^2+2x) is 15x^4+8x^3-108x^2-48x
What is the first derivative of (x^3-12x)(3x^2+2x) ?
The first derivative of (x^3-12x)(3x^2+2x) is 15x^4+8x^3-108x^2-48x