What is the derivative of (6x^2-6x+3(1+2x)) ?

The derivative of (6x^2-6x+3(1+2x)) is 36x^2-12x

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

The first derivative of (6x^2-6x+3(1+2x)) is 36x^2-12x

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

36 x^{2} - 12 x

Solution steps

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

Apply the Product Rule:

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

f = 6 x^{2} - 6 x + 3, g = 1 + 2 x

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

\frac{d}{d x} (6 x^{2} - 6 x + 3) = 12 x - 6

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

= (12 x - 6) (1 + 2 x) + 2 (6 x^{2} - 6 x + 3)

Simplify

(12 x - 6) (1 + 2 x) + 2 (6 x^{2} - 6 x + 3) : 36 x^{2} - 12 x

= 36 x^{2} - 12 x

(2.2) (4.3)

x \to - 2 lim (\frac{x + 3}{x ^{2} - 2})

\int - 7 e^{x} d x

x \to 2 lim (0)

\int (tan (x) - \frac{sin ( x )}{cos ( x )}) d x

What is the derivative of (6x^2-6x+3(1+2x)) ?
The derivative of (6x^2-6x+3(1+2x)) is 36x^2-12x
What is the first derivative of (6x^2-6x+3(1+2x)) ?
The first derivative of (6x^2-6x+3(1+2x)) is 36x^2-12x