What is the derivative of (-3x+12)/(2sqrt(6-x)) ?

The derivative of (-3x+12)/(2sqrt(6-x)) is (3x-24)/(4(6-x)sqrt(6-x))

What is the first derivative of (-3x+12)/(2sqrt(6-x)) ?

The first derivative of (-3x+12)/(2sqrt(6-x)) is (3x-24)/(4(6-x)sqrt(6-x))

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derivative of

\frac{- 3 x + 12}{2 6 - x}

\frac{3 x - 24}{4 ( 6 - x ) 6 - x}

Solution steps

\frac{d}{d x} (\frac{- 3 x + 12}{2 6 - x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (\frac{- 3 x + 12}{6 - x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( - 3 x + 12 ) 6 - x - \frac{d}{d x} ( 6 - x ) ( - 3 x + 12 )}{( 6 - x ) ^{2}}

\frac{d}{d x} (- 3 x + 12) = - 3

\frac{d}{d x} (6 - x) = - \frac{1}{2 6 - x}

= \frac{1}{2} \cdot \frac{( - 3 ) 6 - x - ( - \frac{1}{2 6 - x} ) ( - 3 x + 12 )}{( 6 - x ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( - 3 ) 6 - x - ( - \frac{1}{2 6 - x} ) ( - 3 x + 12 )}{( 6 - x ) ^{2}} : \frac{3 x - 24}{4 ( 6 - x ) 6 - x}

= \frac{3 x - 24}{4 ( 6 - x ) 6 - x}

f (x) = (tan (\frac{1}{x}))^{s e c (\frac{1}{x})}

\int \frac{x}{( 1 + x ^{2} ) ^{y}} d x

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

n = 1 \sum \infty (0.2)^{n - 1}

\int z^{4} d z

What is the derivative of (-3x+12)/(2sqrt(6-x)) ?
The derivative of (-3x+12)/(2sqrt(6-x)) is (3x-24)/(4(6-x)sqrt(6-x))
What is the first derivative of (-3x+12)/(2sqrt(6-x)) ?
The first derivative of (-3x+12)/(2sqrt(6-x)) is (3x-24)/(4(6-x)sqrt(6-x))