What is the derivative of (x^2+3x(x-2)(x^2+1)) ?

The derivative of (x^2+3x(x-2)(x^2+1)) is 5x^4+4x^3-15x^2+2x-6

What is the first derivative of (x^2+3x(x-2)(x^2+1)) ?

The first derivative of (x^2+3x(x-2)(x^2+1)) is 5x^4+4x^3-15x^2+2x-6

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

5 x^{4} + 4 x^{3} - 15 x^{2} + 2 x - 6

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 3 x, g = (x - 2) (x^{2} + 1)

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

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

\frac{d}{d x} ((x - 2) (x^{2} + 1)) = 3 x^{2} - 4 x + 1

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

Simplify

(2 x + 3) (x - 2) (x^{2} + 1) + (3 x^{2} - 4 x + 1) (x^{2} + 3 x) : 5 x^{4} + 4 x^{3} - 15 x^{2} + 2 x - 6

= 5 x^{4} + 4 x^{3} - 15 x^{2} + 2 x - 6

y = 2 x - x^{2}, (0, 2)

9 sin (3 x)

\int_{0}^{1} - x + 2 d x

f (x) = lo g_{3} (4 x^{2} + 2 x)

\frac{- 40 x - 80}{x ^{2} + 3 x + 1}

What is the derivative of (x^2+3x(x-2)(x^2+1)) ?
The derivative of (x^2+3x(x-2)(x^2+1)) is 5x^4+4x^3-15x^2+2x-6
What is the first derivative of (x^2+3x(x-2)(x^2+1)) ?
The first derivative of (x^2+3x(x-2)(x^2+1)) is 5x^4+4x^3-15x^2+2x-6