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

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

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

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

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

3 x^{2} + 2 x - 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 3 x^{2} + 2 x - 1

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