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

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

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

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

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

Solution steps

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

Treat

x, z

as constants

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int e^{- 4 θ} cos (2 θ) d θ

\int tan (X) d X

\frac{d y}{d x} = 4 y

y = \frac{6}{x}

4 t^{2}

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