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Popular >

derivative of (x-1(x-2)(x-3))

Solution

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

Solution

3 x^{2} - 12 x + 11

Solution steps

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

Apply the Product Rule:

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

f = x - 1, g = (x - 2) (x - 3)

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

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

\frac{d}{d x} ((x - 2) (x - 3)) = 2 x - 5

= 1 \cdot (x - 2) (x - 3) + (2 x - 5) (x - 1)

Simplify

1 \cdot (x - 2) (x - 3) + (2 x - 5) (x - 1) : 3 x^{2} - 12 x + 11

= 3 x^{2} - 12 x + 11

Popular Examples

(dP)/(dt)=P(3-P)-9/4

\frac{d P}{d t} = P (3 - P) - \frac{9}{4}

integral from 3 to 8 of t^3ln(2t)

\int_{3}^{8} t^{3} ln (2 t) d t

inverse oflaplace 1/(9s-1)inverse laplace

\frac{1}{9 s - 1}

limit as x approaches 0 of (cos(2x))/x

x \to 0 lim (\frac{cos ( 2 x )}{x})

derivative of (1+x^2^{-1})

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

Frequently Asked Questions (FAQ)

What is the derivative of (x-1(x-2)(x-3)) ?
The derivative of (x-1(x-2)(x-3)) is 3x^2-12x+11
What is the first derivative of (x-1(x-2)(x-3)) ?
The first derivative of (x-1(x-2)(x-3)) is 3x^2-12x+11