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

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

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

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

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derivative of

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

3 x^{2} + 8 x - 4

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

1 \cdot (x^{2} - 4) + 2 x (x + 4) : 3 x^{2} + 8 x - 4

= 3 x^{2} + 8 x - 4

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

x^{2} - 1, [- 1, 2]

\frac{d ^{2}}{d x ^{2}} (2 csc (x))

x \to 4 lim (x^{2} - 5)

\int \frac{1}{x ( 2 x + 1 )} d x

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