What is (\partial)/(\partial x)((2x^2)/((2x+7y)^2)) ?

The answer to (\partial)/(\partial x)((2x^2)/((2x+7y)^2)) is (28xy)/((2x+7y)^3)

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(\partial)/(\partial x)((2x^2)/((2x+7y)^2))

\frac{\partial}{\partial x} (\frac{2 x ^{2}}{( 2 x + 7 y ) ^{2}})

\frac{28 x y}{( 2 x + 7 y ) ^{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{2 x ^{2}}{( 2 x + 7 y ) ^{2}})

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (\frac{x ^{2}}{( 2 x + 7 y ) ^{2}})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{\partial}{\partial x} ( x ^{2} ) ( 2 x + 7 y ) ^{2} - \frac{\partial}{\partial x} ( ( 2 x + 7 y ) ^{2} ) x ^{2}}{( ( 2 x + 7 y ) ^{2} ) ^{2}}

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} ((2 x + 7 y)^{2}) = 4 (2 x + 7 y)

= 2 \cdot \frac{2 x ( 2 x + 7 y ) ^{2} - 4 ( 2 x + 7 y ) x ^{2}}{( ( 2 x + 7 y ) ^{2} ) ^{2}}

Simplify

2 \cdot \frac{2 x ( 2 x + 7 y ) ^{2} - 4 ( 2 x + 7 y ) x ^{2}}{( ( 2 x + 7 y ) ^{2} ) ^{2}} : \frac{28 x y}{( 2 x + 7 y ) ^{3}}

= \frac{28 x y}{( 2 x + 7 y ) ^{3}}

x \to - 3 lim (∣ - x - 1 ∣)

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

\frac{6}{5} - \frac{6}{5} e^{- 20 t}

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

\frac{x ^{2} + 1}{x ^{2} - 4}

What is (\partial)/(\partial x)((2x^2)/((2x+7y)^2)) ?
The answer to (\partial)/(\partial x)((2x^2)/((2x+7y)^2)) is (28xy)/((2x+7y)^3)