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

The answer to (\partial)/(\partial x)((y+x)/(y+z)) is 1/(y+z)

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

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

\frac{1}{y + z}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (y) = 0

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

= \frac{1}{y + z} (0 + 1)

Simplify

= \frac{1}{y + z}

\frac{\partial}{\partial x} (ln (x) - 2)

x \to 1 lim (\frac{2 x}{x ^{2} + x})

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

\frac{d}{d x} ((2 x^{2} + 1)^{4})

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

What is (\partial)/(\partial x)((y+x)/(y+z)) ?
The answer to (\partial)/(\partial x)((y+x)/(y+z)) is 1/(y+z)