What is the derivative of f(x)=(2x+3)(x^2-4) ?

The derivative of f(x)=(2x+3)(x^2-4) is 6x^2+6x-8

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

The first derivative of f(x)=(2x+3)(x^2-4) is 6x^2+6x-8

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derivative of

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

6 x^{2} + 6 x - 8

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 (x^{2} - 4) + 2 x (2 x + 3) : 6 x^{2} + 6 x - 8

= 6 x^{2} + 6 x - 8

What is the derivative of f(x)=(2x+3)(x^2-4) ?
The derivative of f(x)=(2x+3)(x^2-4) is 6x^2+6x-8
What is the first derivative of f(x)=(2x+3)(x^2-4) ?
The first derivative of f(x)=(2x+3)(x^2-4) is 6x^2+6x-8