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

The derivative of (-x+6/(2(2-x)sqrt(2-x))) is (-x+14)/(4(-x+2)^{5/2)}

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

The first derivative of (-x+6/(2(2-x)sqrt(2-x))) is (-x+14)/(4(-x+2)^{5/2)}

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

\frac{- x + 14}{4 ( - x + 2 ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

\frac{1}{2} \cdot \frac{( - 1 ) ( 2 - x ) 2 - x - ( - \frac{3 2 - x}{2} ) ( - x + 6 )}{( ( 2 - x ) 2 - x ) ^{2}} : \frac{- x + 14}{4 ( - x + 2 ) ^{\frac{5}{2}}}

= \frac{- x + 14}{4 ( - x + 2 ) ^{\frac{5}{2}}}

n = 0 \sum \infty \frac{4}{2 n + 1}

f (x) = 6 x e^{x}, (0, 0)

y = tan (2 x)

\frac{\partial}{\partial x} (- 3 sin (3 x))

4 x - \frac{x ^{3}}{4}

What is the derivative of (-x+6/(2(2-x)sqrt(2-x))) ?
The derivative of (-x+6/(2(2-x)sqrt(2-x))) is (-x+14)/(4(-x+2)^{5/2)}
What is the first derivative of (-x+6/(2(2-x)sqrt(2-x))) ?
The first derivative of (-x+6/(2(2-x)sqrt(2-x))) is (-x+14)/(4(-x+2)^{5/2)}