What is the derivative of x*sqrt(9-x) ?

The derivative of x*sqrt(9-x) is (-3x+18)/(2sqrt(9-x))

What is the first derivative of x*sqrt(9-x) ?

The first derivative of x*sqrt(9-x) is (-3x+18)/(2sqrt(9-x))

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\frac{d}{d x} (x \cdot 9 - x)

\frac{- 3 x + 18}{2 9 - x}

Solution steps

\frac{d}{d x} (x 9 - x)

Apply the Product Rule:

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

f = x, g = 9 - x

= \frac{d x}{d x} 9 - x + \frac{d}{d x} (9 - x) x

\frac{d x}{d x} = 1

\frac{d}{d x} (9 - x) = - \frac{1}{2 9 - x}

= 1 \cdot 9 - x + (- \frac{1}{2 9 - x}) x

Simplify

1 \cdot 9 - x + (- \frac{1}{2 9 - x}) x : \frac{- 3 x + 18}{2 9 - x}

= \frac{- 3 x + 18}{2 9 - x}

What is the derivative of x*sqrt(9-x) ?
The derivative of x*sqrt(9-x) is (-3x+18)/(2sqrt(9-x))
What is the first derivative of x*sqrt(9-x) ?
The first derivative of x*sqrt(9-x) is (-3x+18)/(2sqrt(9-x))