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

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

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

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

\frac{1}{y + z}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{y + z}

\frac{d y}{d x} = \frac{y x}{x - 1}

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y^{^{'}} + 5 y = 2 x y^{5}

\frac{d y}{d x} + 2 x^{- 1} y = 6 x^{4} y^{2}

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