What is (\partial)/(\partial x)((3x+9)/(2-x)) ?

The answer to (\partial)/(\partial x)((3x+9)/(2-x)) is (15)/((2-x)^2)

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(\partial)/(\partial x)((3x+9)/(2-x))

\frac{\partial}{\partial x} (\frac{3 x + 9}{2 - x})

\frac{15}{( 2 - x ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{3 x + 9}{2 - x})

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( 3 x + 9 ) ( 2 - x ) - \frac{\partial}{\partial x} ( 2 - x ) ( 3 x + 9 )}{( 2 - x ) ^{2}}

\frac{\partial}{\partial x} (3 x + 9) = 3

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

= \frac{3 ( 2 - x ) - ( - 1 ) ( 3 x + 9 )}{( 2 - x ) ^{2}}

Simplify

\frac{3 ( 2 - x ) - ( - 1 ) ( 3 x + 9 )}{( 2 - x ) ^{2}} : \frac{15}{( 2 - x ) ^{2}}

= \frac{15}{( 2 - x ) ^{2}}

\frac{d}{d x} (\frac{6 x}{x + 5})

f (x) = \frac{x ^{2}}{4}

x + x y^{^{'}} = y

\int e^{- 5 x} cos (3 x) d x

\frac{5}{2} + \frac{3}{2} x

What is (\partial)/(\partial x)((3x+9)/(2-x)) ?
The answer to (\partial)/(\partial x)((3x+9)/(2-x)) is (15)/((2-x)^2)