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

The derivative of f(x)=x(2x-1)(3x+2) is 18x^2+2x-2

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

The first derivative of f(x)=x(2x-1)(3x+2) is 18x^2+2x-2

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derivative of

f (x) = x (2 x - 1) (3 x + 2)

18 x^{2} + 2 x - 2

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((2 x - 1) (3 x + 2)) = 12 x + 1

= 1 \cdot (2 x - 1) (3 x + 2) + (12 x + 1) x

Simplify

1 \cdot (2 x - 1) (3 x + 2) + (12 x + 1) x : 18 x^{2} + 2 x - 2

= 18 x^{2} + 2 x - 2

What is the derivative of f(x)=x(2x-1)(3x+2) ?
The derivative of f(x)=x(2x-1)(3x+2) is 18x^2+2x-2
What is the first derivative of f(x)=x(2x-1)(3x+2) ?
The first derivative of f(x)=x(2x-1)(3x+2) is 18x^2+2x-2