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

The derivative of (x+2/(sqrt(2-x))) is (-x+6)/(2(2-x)sqrt(2-x))

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

The first derivative of (x+2/(sqrt(2-x))) is (-x+6)/(2(2-x)sqrt(2-x))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial k} (ln (sin (\frac{x}{k})))

\int \frac{x ^{2}}{4 x ^{3} + 7} d x

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{1}{x}))

(x^{2} - x) y^{^{'}} = y - 2 x y

cos^{4} (θ + 5)

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