What is the derivative of (x-2)(x+1)(x+6) ?

The derivative of (x-2)(x+1)(x+6) is 3x^2+10x-8

What is the first derivative of (x-2)(x+1)(x+6) ?

The first derivative of (x-2)(x+1)(x+6) is 3x^2+10x-8

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derivative of

(x - 2) (x + 1) (x + 6)

3 x^{2} + 10 x - 8

Solution steps

\frac{d}{d x} ((x - 2) (x + 1) (x + 6))

Apply the Product Rule:

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

f = x - 2, g = (x + 1) (x + 6)

= \frac{d}{d x} (x - 2) (x + 1) (x + 6) + \frac{d}{d x} ((x + 1) (x + 6)) (x - 2)

\frac{d}{d x} (x - 2) = 1

\frac{d}{d x} ((x + 1) (x + 6)) = 2 x + 7

= 1 \cdot (x + 1) (x + 6) + (2 x + 7) (x - 2)

Simplify

1 \cdot (x + 1) (x + 6) + (2 x + 7) (x - 2) : 3 x^{2} + 10 x - 8

= 3 x^{2} + 10 x - 8

What is the derivative of (x-2)(x+1)(x+6) ?
The derivative of (x-2)(x+1)(x+6) is 3x^2+10x-8
What is the first derivative of (x-2)(x+1)(x+6) ?
The first derivative of (x-2)(x+1)(x+6) is 3x^2+10x-8