What is (\partial)/(\partial x)((3x-5)/(2x+4)) ?

The answer to (\partial)/(\partial x)((3x-5)/(2x+4)) is (11)/(2(x+2)^2)

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(\partial)/(\partial x)((3x-5)/(2x+4))

\frac{\partial}{\partial x} (\frac{3 x - 5}{2 x + 4})

\frac{11}{2 ( x + 2 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{3 x - 5}{2 x + 4})

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (3 x - 5) = 3

\frac{\partial}{\partial x} (2 x + 4) = 2

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

Simplify

\frac{3 ( 2 x + 4 ) - 2 ( 3 x - 5 )}{( 2 x + 4 ) ^{2}} : \frac{11}{2 ( x + 2 ) ^{2}}

= \frac{11}{2 ( x + 2 ) ^{2}}

x \to 0 + lim (\frac{14 x ^{3} + 15 x}{x})

\int - 4 sin (4 t) d t

\frac{d y}{d x} = 6 e^{x}

\frac{\partial}{\partial t} (- 2 s^{2} + t^{2})

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

What is (\partial)/(\partial x)((3x-5)/(2x+4)) ?
The answer to (\partial)/(\partial x)((3x-5)/(2x+4)) is (11)/(2(x+2)^2)