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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (4 x - 5)

\frac{1}{3 - 2 x}

\frac{d ^{4}}{d x ^{4}} (\frac{1}{x})

y = \frac{x ^{2}}{x ^{3} - 3 x}, y = \frac{1}{x ^{3} - 3 x}, 2, 21

\frac{d ^{2}}{d x ^{2}} (2 e^{- \frac{x}{4}})

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