What is (\partial)/(\partial x)((5x)/((x+y)^3)) ?

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

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(\partial)/(\partial x)((5x)/((x+y)^3))

\frac{\partial}{\partial x} (\frac{5 x}{( x + y ) ^{3}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{5 x}{( x + y ) ^{3}})

Treat

y

as a constant

Take the constant out:

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

= 5 \frac{\partial}{\partial x} (\frac{x}{( x + y ) ^{3}})

Apply the Quotient Rule:

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

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

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

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

= 5 \cdot \frac{1 \cdot ( x + y ) ^{3} - 3 ( x + y ) ^{2} x}{( ( x + y ) ^{3} ) ^{2}}

Simplify

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

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

\int \frac{81 - x ^{2}}{x} d x

\int_{0}^{3} 5 - (x - 1)^{2} d x

\frac{\partial}{\partial x} (a x)

\int_{x}^{1} 2 d y

\frac{d}{d x} (ln (sec (x) + tan (x)) sin (x))

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