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Popular >

derivative of f(x)=(2x+3)(x^2+2x)

Solution

derivative of

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

Solution

6 x^{2} + 14 x + 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 (x^{2} + 2 x) + (2 x + 2) (2 x + 3) : 6 x^{2} + 14 x + 6

= 6 x^{2} + 14 x + 6

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(2x+3)(x^2+2x) ?
The derivative of f(x)=(2x+3)(x^2+2x) is 6x^2+14x+6
What is the first derivative of f(x)=(2x+3)(x^2+2x) ?
The first derivative of f(x)=(2x+3)(x^2+2x) is 6x^2+14x+6