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Popular >

derivative of f(x)=(x^2+3x)(x+4)

Solution

derivative of

f (x) = (x^{2} + 3 x) (x + 4)

Solution

3 x^{2} + 14 x + 12

Solution steps

\frac{d}{d x} ((x^{2} + 3 x) (x + 4))

Apply the Product Rule:

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

f = x^{2} + 3 x, g = x + 4

= \frac{d}{d x} (x^{2} + 3 x) (x + 4) + \frac{d}{d x} (x + 4) (x^{2} + 3 x)

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

\frac{d}{d x} (x + 4) = 1

= (2 x + 3) (x + 4) + 1 \cdot (x^{2} + 3 x)

Simplify

(2 x + 3) (x + 4) + 1 \cdot (x^{2} + 3 x) : 3 x^{2} + 14 x + 12

= 3 x^{2} + 14 x + 12

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2+3x)(x+4) ?
The derivative of f(x)=(x^2+3x)(x+4) is 3x^2+14x+12
What is the first derivative of f(x)=(x^2+3x)(x+4) ?
The first derivative of f(x)=(x^2+3x)(x+4) is 3x^2+14x+12