What is the derivative of (x-a(x-b)(x-c)) ?

The derivative of (x-a(x-b)(x-c)) is 3x^2-2ax-2bx-2cx+ab+bc+ac

What is the first derivative of (x-a(x-b)(x-c)) ?

The first derivative of (x-a(x-b)(x-c)) is 3x^2-2ax-2bx-2cx+ab+bc+ac

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\frac{d}{d x} ((x - a) (x - b) (x - c))

3 x^{2} - 2 a x - 2 b x - 2 c x + ab + b c + a c

Solution steps

\frac{d}{d x} ((x - a) (x - b) (x - c))

Apply the Product Rule:

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

f = x - a, g = (x - b) (x - c)

= \frac{d}{d x} (x - a) (x - b) (x - c) + \frac{d}{d x} ((x - b) (x - c)) (x - a)

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

\frac{d}{d x} ((x - b) (x - c)) = 2 x - b - c

= 1 \cdot (x - b) (x - c) + (2 x - b - c) (x - a)

Simplify

1 \cdot (x - b) (x - c) + (2 x - b - c) (x - a) : 3 x^{2} - 2 a x - 2 b x - 2 c x + ab + b c + a c

= 3 x^{2} - 2 a x - 2 b x - 2 c x + ab + b c + a c

\frac{d y}{d t} + \frac{4 y}{200 + 3 t} = 8

f (x) = 2 sec^{2} (x) tan (x)

\int \frac{21}{( x ^{2} - 1 ) ^{2}} d x

\frac{d}{d t} (e^{- 2 t} y (t))

2 sin (2 x)

What is the derivative of (x-a(x-b)(x-c)) ?
The derivative of (x-a(x-b)(x-c)) is 3x^2-2ax-2bx-2cx+ab+bc+ac
What is the first derivative of (x-a(x-b)(x-c)) ?
The first derivative of (x-a(x-b)(x-c)) is 3x^2-2ax-2bx-2cx+ab+bc+ac