What is (\partial)/(\partial x)((9xz)/(x+y)) ?

The answer to (\partial)/(\partial x)((9xz)/(x+y)) is (9zy)/((x+y)^2)

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(\partial)/(\partial x)((9xz)/(x+y))

\frac{\partial}{\partial x} (\frac{9 x z}{x + y})

\frac{9 zy}{( x + y ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{9 x z}{x + y})

Treat

z, y

as constants

Take the constant out:

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

= 9 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}}

= 9 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

= 9 z \frac{1 \cdot ( x + y ) - 1 \cdot x}{( x + y ) ^{2}}

Simplify

9 z \frac{1 \cdot ( x + y ) - 1 \cdot x}{( x + y ) ^{2}} : \frac{9 zy}{( x + y ) ^{2}}

= \frac{9 zy}{( x + y ) ^{2}}

\int \frac{x ^{2} - 6 x - 17}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

\int_{0}^{3} (9 - x^{2}) d x

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)

f (x) = x \cdot 2 x + 2

y^{^{'}} = e^{(x + y)}

What is (\partial)/(\partial x)((9xz)/(x+y)) ?
The answer to (\partial)/(\partial x)((9xz)/(x+y)) is (9zy)/((x+y)^2)