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

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

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

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

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

3 x^{2} - 3

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 3 x^{2} - 3

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