What is (\partial)/(\partial x)((2x-2z)/(y+2z)) ?

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

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(\partial)/(\partial x)((2x-2z)/(y+2z))

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

\frac{2}{y + 2 z}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (2 z) = 0

= \frac{1}{y + 2 z} (2 - 0)

Simplify

\frac{1}{y + 2 z} (2 - 0) : \frac{2}{y + 2 z}

= \frac{2}{y + 2 z}

- 5 sin (3 t)

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

\int - e^{x} x d x

\int \frac{36}{1 + 36 x ^{2}} d x

y^{^{'}} = 1 - 2 y

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