What is the derivative of (x-1(x^2-8x+7)) ?

The derivative of (x-1(x^2-8x+7)) is 3x^2-18x+15

What is the first derivative of (x-1(x^2-8x+7)) ?

The first derivative of (x-1(x^2-8x+7)) is 3x^2-18x+15

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\frac{d}{d x} ((x - 1) (x^{2} - 8 x + 7))

3 x^{2} - 18 x + 15

Solution steps

\frac{d}{d x} ((x - 1) (x^{2} - 8 x + 7))

Apply the Product Rule:

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

f = x - 1, g = x^{2} - 8 x + 7

= \frac{d}{d x} (x - 1) (x^{2} - 8 x + 7) + \frac{d}{d x} (x^{2} - 8 x + 7) (x - 1)

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

\frac{d}{d x} (x^{2} - 8 x + 7) = 2 x - 8

= 1 \cdot (x^{2} - 8 x + 7) + (2 x - 8) (x - 1)

Simplify

1 \cdot (x^{2} - 8 x + 7) + (2 x - 8) (x - 1) : 3 x^{2} - 18 x + 15

= 3 x^{2} - 18 x + 15

What is the derivative of (x-1(x^2-8x+7)) ?
The derivative of (x-1(x^2-8x+7)) is 3x^2-18x+15
What is the first derivative of (x-1(x^2-8x+7)) ?
The first derivative of (x-1(x^2-8x+7)) is 3x^2-18x+15