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

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

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

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

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derivative of

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

3 x^{2} - 10 x + 8

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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