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

The derivative of (x^2-2x+1(x^3-1)) is 5x^4-8x^3+3x^2-2x+2

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

The first derivative of (x^2-2x+1(x^3-1)) is 5x^4-8x^3+3x^2-2x+2

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\frac{d}{d x} ((x^{2} - 2 x + 1) (x^{3} - 1))

5 x^{4} - 8 x^{3} + 3 x^{2} - 2 x + 2

Solution steps

\frac{d}{d x} ((x^{2} - 2 x + 1) (x^{3} - 1))

Apply the Product Rule:

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

f = x^{2} - 2 x + 1, g = x^{3} - 1

= \frac{d}{d x} (x^{2} - 2 x + 1) (x^{3} - 1) + \frac{d}{d x} (x^{3} - 1) (x^{2} - 2 x + 1)

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

\frac{d}{d x} (x^{3} - 1) = 3 x^{2}

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

Simplify

(2 x - 2) (x^{3} - 1) + 3 x^{2} (x^{2} - 2 x + 1) : 5 x^{4} - 8 x^{3} + 3 x^{2} - 2 x + 2

= 5 x^{4} - 8 x^{3} + 3 x^{2} - 2 x + 2

What is the derivative of (x^2-2x+1(x^3-1)) ?
The derivative of (x^2-2x+1(x^3-1)) is 5x^4-8x^3+3x^2-2x+2
What is the first derivative of (x^2-2x+1(x^3-1)) ?
The first derivative of (x^2-2x+1(x^3-1)) is 5x^4-8x^3+3x^2-2x+2