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

The derivative of 3(x^2+3x+1)^2(2x+3) is 3(10x^4+60x^3+120x^2+90x+20)

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

The first derivative of 3(x^2+3x+1)^2(2x+3) is 3(10x^4+60x^3+120x^2+90x+20)

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derivative of

3 (x^{2} + 3 x + 1)^{2} (2 x + 3)

3 (10 x^{4} + 60 x^{3} + 120 x^{2} + 90 x + 20)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 (2 (x^{2} + 3 x + 1) (2 x + 3) (2 x + 3) + 2 (x^{2} + 3 x + 1)^{2}) : 3 (10 x^{4} + 60 x^{3} + 120 x^{2} + 90 x + 20)

= 3 (10 x^{4} + 60 x^{3} + 120 x^{2} + 90 x + 20)

2 x^{7}

\frac{\partial}{\partial x} (sin (3 x) cos (4 y))

(- 3.1) (- 17.2)

\int_{0}^{2} x^{2} e^{x} d x

e^{3}

What is the derivative of 3(x^2+3x+1)^2(2x+3) ?
The derivative of 3(x^2+3x+1)^2(2x+3) is 3(10x^4+60x^3+120x^2+90x+20)
What is the first derivative of 3(x^2+3x+1)^2(2x+3) ?
The first derivative of 3(x^2+3x+1)^2(2x+3) is 3(10x^4+60x^3+120x^2+90x+20)