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Popular >

derivative of (2x+1(3x^2+6))

Solution

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

Solution

18 x^{2} + 6 x + 12

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 (3 x^{2} + 6) + 6 x (2 x + 1) : 18 x^{2} + 6 x + 12

= 18 x^{2} + 6 x + 12

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Frequently Asked Questions (FAQ)

What is the derivative of (2x+1(3x^2+6)) ?
The derivative of (2x+1(3x^2+6)) is 18x^2+6x+12
What is the first derivative of (2x+1(3x^2+6)) ?
The first derivative of (2x+1(3x^2+6)) is 18x^2+6x+12