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

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

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

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

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derivative of

(x + 1) (x - 2)^{2}

3 x^{2} - 6 x

Solution steps

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

Apply the Product Rule:

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

f = x + 1, g = (x - 2)^{2}

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

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

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

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

Simplify

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

= 3 x^{2} - 6 x

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