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Popular >

derivative of f(x)=(x^2-4)(3x+1)

Solution

derivative of

f (x) = (x^{2} - 4) (3 x + 1)

Solution

9 x^{2} + 2 x - 12

Solution steps

\frac{d}{d x} ((x^{2} - 4) (3 x + 1))

Apply the Product Rule:

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

f = x^{2} - 4, g = 3 x + 1

= \frac{d}{d x} (x^{2} - 4) (3 x + 1) + \frac{d}{d x} (3 x + 1) (x^{2} - 4)

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

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

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

Simplify

2 x (3 x + 1) + 3 (x^{2} - 4) : 9 x^{2} + 2 x - 12

= 9 x^{2} + 2 x - 12

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2-4)(3x+1) ?
The derivative of f(x)=(x^2-4)(3x+1) is 9x^2+2x-12
What is the first derivative of f(x)=(x^2-4)(3x+1) ?
The first derivative of f(x)=(x^2-4)(3x+1) is 9x^2+2x-12