What is (\partial)/(\partial x)(((xy))/((x+y))) ?

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

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(\partial)/(\partial x)(((xy))/((x+y)))

\frac{\partial}{\partial x} (\frac{( x y )}{( x + y )})

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

Solution steps

\frac{\partial}{\partial x} (\frac{( x y )}{( x + y )})

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (\frac{x}{x + y})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (9 cos (9 x))

f (x) = cos (x^{l n (x^{2} + 1)})

n = 0 \sum \infty \frac{n !}{3 ^{n}}

\int 103 t^{2} d t

\frac{d}{d x} (9 x + \frac{1}{x} - 4)

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