What is the derivative of (x-3)sqrt(4-x) ?

The derivative of (x-3)sqrt(4-x) is (-3x+11)/(2sqrt(4-x))

What is the first derivative of (x-3)sqrt(4-x) ?

The first derivative of (x-3)sqrt(4-x) is (-3x+11)/(2sqrt(4-x))

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derivative of

(x - 3) 4 - x

\frac{- 3 x + 11}{2 4 - x}

Solution steps

\frac{d}{d x} ((x - 3) 4 - x)

Apply the Product Rule:

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

f = x - 3, g = 4 - x

= \frac{d}{d x} (x - 3) 4 - x + \frac{d}{d x} (4 - x) (x - 3)

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

\frac{d}{d x} (4 - x) = - \frac{1}{2 4 - x}

= 1 \cdot 4 - x + (- \frac{1}{2 4 - x}) (x - 3)

Simplify

1 \cdot 4 - x + (- \frac{1}{2 4 - x}) (x - 3) : \frac{- 3 x + 11}{2 4 - x}

= \frac{- 3 x + 11}{2 4 - x}

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

ln (x), 5

x \to - \infty lim (x^{n})

F (x) = \frac{x ^{3} - 3 x ^{2} + 4 x - 5}{x ^{2}}

f (x) = e^{- x^{2}} + x

What is the derivative of (x-3)sqrt(4-x) ?
The derivative of (x-3)sqrt(4-x) is (-3x+11)/(2sqrt(4-x))
What is the first derivative of (x-3)sqrt(4-x) ?
The first derivative of (x-3)sqrt(4-x) is (-3x+11)/(2sqrt(4-x))