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

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

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

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

\frac{1}{y - z}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{y - z}

n = 0 \sum \infty (- \frac{3}{2})^{n}

y = 5 x - x^{2}, y = x

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

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

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