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

The answer to (\partial)/(\partial x)((5xz)/(x+y)) is (5zy)/((x+y)^2)

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(\partial)/(\partial x)((5xz)/(x+y))

\frac{\partial}{\partial x} (\frac{5 x z}{x + y})

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

Solution steps

\frac{\partial}{\partial x} (\frac{5 x z}{x + y})

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 5 z \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

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

Simplify

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

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

x \to 0 lim (\frac{5 x ^{2} - 6 x}{x})

\frac{1}{( s + 2 ) ( s + 1 )}

(2 x^{2} - 7)^{- 1}

\int \frac{1}{x ln ( x ^{8} )} d x

\frac{d y}{d x} = \frac{6 y ^{2} + 5 x ^{2}}{x y}

What is (\partial)/(\partial x)((5xz)/(x+y)) ?
The answer to (\partial)/(\partial x)((5xz)/(x+y)) is (5zy)/((x+y)^2)