What is the derivative of f(x)=(12-x)sqrt(24x-144) ?

The derivative of f(x)=(12-x)sqrt(24x-144) is (-36x+288)/(sqrt(24x-144))

What is the first derivative of f(x)=(12-x)sqrt(24x-144) ?

The first derivative of f(x)=(12-x)sqrt(24x-144) is (-36x+288)/(sqrt(24x-144))

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derivative of

f (x) = (12 - x) 24 x - 144

\frac{- 36 x + 288}{24 x - 144}

Solution steps

\frac{d}{d x} ((12 - x) 24 x - 144)

Apply the Product Rule:

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

f = 12 - x, g = 24 x - 144

= \frac{d}{d x} (12 - x) 24 x - 144 + \frac{d}{d x} (24 x - 144) (12 - x)

\frac{d}{d x} (12 - x) = - 1

\frac{d}{d x} (24 x - 144) = \frac{12}{24 x - 144}

= (- 1) 24 x - 144 + \frac{12}{24 x - 144} (12 - x)

Simplify

(- 1) 24 x - 144 + \frac{12}{24 x - 144} (12 - x) : \frac{- 36 x + 288}{24 x - 144}

= \frac{- 36 x + 288}{24 x - 144}

What is the derivative of f(x)=(12-x)sqrt(24x-144) ?
The derivative of f(x)=(12-x)sqrt(24x-144) is (-36x+288)/(sqrt(24x-144))
What is the first derivative of f(x)=(12-x)sqrt(24x-144) ?
The first derivative of f(x)=(12-x)sqrt(24x-144) is (-36x+288)/(sqrt(24x-144))