What is the derivative of (4x^2-x(x^3-8x^2+12)) ?

The derivative of (4x^2-x(x^3-8x^2+12)) is 20x^4-132x^3+24x^2+96x-12

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

The first derivative of (4x^2-x(x^3-8x^2+12)) is 20x^4-132x^3+24x^2+96x-12

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\frac{d}{d x} ((4 x^{2} - x) (x^{3} - 8 x^{2} + 12))

20 x^{4} - 132 x^{3} + 24 x^{2} + 96 x - 12

Solution steps

\frac{d}{d x} ((4 x^{2} - x) (x^{3} - 8 x^{2} + 12))

Apply the Product Rule:

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

f = 4 x^{2} - x, g = x^{3} - 8 x^{2} + 12

= \frac{d}{d x} (4 x^{2} - x) (x^{3} - 8 x^{2} + 12) + \frac{d}{d x} (x^{3} - 8 x^{2} + 12) (4 x^{2} - x)

\frac{d}{d x} (4 x^{2} - x) = 8 x - 1

\frac{d}{d x} (x^{3} - 8 x^{2} + 12) = 3 x^{2} - 16 x

= (8 x - 1) (x^{3} - 8 x^{2} + 12) + (3 x^{2} - 16 x) (4 x^{2} - x)

Simplify

(8 x - 1) (x^{3} - 8 x^{2} + 12) + (3 x^{2} - 16 x) (4 x^{2} - x) : 20 x^{4} - 132 x^{3} + 24 x^{2} + 96 x - 12

= 20 x^{4} - 132 x^{3} + 24 x^{2} + 96 x - 12

f (x) = x^{2} + 3

x \to 1 lim (4 x - \frac{4}{x - 1})

\int x^{p} ln (x) d x

f (x) = (x^{2} + 9)^{\frac{1}{2}}

5^{y}

What is the derivative of (4x^2-x(x^3-8x^2+12)) ?
The derivative of (4x^2-x(x^3-8x^2+12)) is 20x^4-132x^3+24x^2+96x-12
What is the first derivative of (4x^2-x(x^3-8x^2+12)) ?
The first derivative of (4x^2-x(x^3-8x^2+12)) is 20x^4-132x^3+24x^2+96x-12