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

The derivative of (2x^3+2)(x^4-3x) is 14x^6-16x^3-6

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

The first derivative of (2x^3+2)(x^4-3x) is 14x^6-16x^3-6

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derivative of

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

14 x^{6} - 16 x^{3} - 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 6 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (2 x^{3} + 2)

Simplify

6 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (2 x^{3} + 2) : 14 x^{6} - 16 x^{3} - 6

= 14 x^{6} - 16 x^{3} - 6

\int \frac{x}{x ^{2} - 1} d x

\frac{d}{d x} (a^{c o s (x)})

\int \frac{u + 1}{u ^{2} + 1} d u

f (x) = cos^{4} (sin^{3} (x))

f (x) = x^{4} + 7 x^{2} - x, at x = 1

What is the derivative of (2x^3+2)(x^4-3x) ?
The derivative of (2x^3+2)(x^4-3x) is 14x^6-16x^3-6
What is the first derivative of (2x^3+2)(x^4-3x) ?
The first derivative of (2x^3+2)(x^4-3x) is 14x^6-16x^3-6