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Popular >

derivative of (3x^2+3x-1*(2x+3))

Solution

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

Solution

18 x^{2} + 30 x + 7

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

(6 x + 3) (2 x + 3) + 2 (3 x^{2} + 3 x - 1) : 18 x^{2} + 30 x + 7

= 18 x^{2} + 30 x + 7

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^2+3x-1*(2x+3)) ?
The derivative of (3x^2+3x-1*(2x+3)) is 18x^2+30x+7
What is the first derivative of (3x^2+3x-1*(2x+3)) ?
The first derivative of (3x^2+3x-1*(2x+3)) is 18x^2+30x+7