What is the derivative of f(x)=(x-2)(3-2x)(6-x) ?

The derivative of f(x)=(x-2)(3-2x)(6-x) is 6x^2-38x+48

What is the first derivative of f(x)=(x-2)(3-2x)(6-x) ?

The first derivative of f(x)=(x-2)(3-2x)(6-x) is 6x^2-38x+48

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derivative of

f (x) = (x - 2) (3 - 2 x) (6 - x)

6 x^{2} - 38 x + 48

Solution steps

\frac{d}{d x} ((x - 2) (3 - 2 x) (6 - x))

Apply the Product Rule:

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

f = x - 2, g = (3 - 2 x) (6 - x)

= \frac{d}{d x} (x - 2) (3 - 2 x) (6 - x) + \frac{d}{d x} ((3 - 2 x) (6 - x)) (x - 2)

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

\frac{d}{d x} ((3 - 2 x) (6 - x)) = 4 x - 15

= 1 \cdot (3 - 2 x) (6 - x) + (4 x - 15) (x - 2)

Simplify

1 \cdot (3 - 2 x) (6 - x) + (4 x - 15) (x - 2) : 6 x^{2} - 38 x + 48

= 6 x^{2} - 38 x + 48

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4 x^{4} - \frac{1}{4 x ^{4}}

\frac{\partial}{\partial x} (\frac{- 9 x - 7 y}{( 5 x + 3 y )})

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What is the derivative of f(x)=(x-2)(3-2x)(6-x) ?
The derivative of f(x)=(x-2)(3-2x)(6-x) is 6x^2-38x+48
What is the first derivative of f(x)=(x-2)(3-2x)(6-x) ?
The first derivative of f(x)=(x-2)(3-2x)(6-x) is 6x^2-38x+48