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

The derivative of (x^3+3x^2+x-1(2x^2-x+1)) is 10x^4+20x^3+2

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

The first derivative of (x^3+3x^2+x-1(2x^2-x+1)) is 10x^4+20x^3+2

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

10 x^{4} + 20 x^{3} + 2

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{3} + 3 x^{2} + x - 1) = 3 x^{2} + 6 x + 1

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

= (3 x^{2} + 6 x + 1) (2 x^{2} - x + 1) + (4 x - 1) (x^{3} + 3 x^{2} + x - 1)

Simplify

(3 x^{2} + 6 x + 1) (2 x^{2} - x + 1) + (4 x - 1) (x^{3} + 3 x^{2} + x - 1) : 10 x^{4} + 20 x^{3} + 2

= 10 x^{4} + 20 x^{3} + 2

y = \frac{1}{3} - 6

co sin (o)

\frac{\partial}{\partial x} (ln (x + 6 y + 4 z))

(s^{5} - 9)^{2}

\frac{d}{d x} (arctan (9 x))

What is the derivative of (x^3+3x^2+x-1(2x^2-x+1)) ?
The derivative of (x^3+3x^2+x-1(2x^2-x+1)) is 10x^4+20x^3+2
What is the first derivative of (x^3+3x^2+x-1(2x^2-x+1)) ?
The first derivative of (x^3+3x^2+x-1(2x^2-x+1)) is 10x^4+20x^3+2