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

The derivative of f(x)=(2x^2-x+1)*(x^2+2x+3) is 8x^3+9x^2+10x-1

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

The first derivative of f(x)=(2x^2-x+1)*(x^2+2x+3) is 8x^3+9x^2+10x-1

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derivative of

f (x) = (2 x^{2} - x + 1) \cdot (x^{2} + 2 x + 3)

8 x^{3} + 9 x^{2} + 10 x - 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(4 x - 1) (x^{2} + 2 x + 3) + (2 x + 2) (2 x^{2} - x + 1) : 8 x^{3} + 9 x^{2} + 10 x - 1

= 8 x^{3} + 9 x^{2} + 10 x - 1

\int \frac{1}{( x - 1 ) ( x + 4 )} d x

x^{2} \cdot arctan (x)

x \to 0 + lim (5 x^{s i n (x)})

cos (x) \frac{π}{2}

y^{^{'}} = a y + b

What is the derivative of f(x)=(2x^2-x+1)*(x^2+2x+3) ?
The derivative of f(x)=(2x^2-x+1)*(x^2+2x+3) is 8x^3+9x^2+10x-1
What is the first derivative of f(x)=(2x^2-x+1)*(x^2+2x+3) ?
The first derivative of f(x)=(2x^2-x+1)*(x^2+2x+3) is 8x^3+9x^2+10x-1