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

The answer to (\partial)/(\partial x)(sqrt(y-x)-z) is -1/(2sqrt(y-x))

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

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

- \frac{1}{2 y - x}

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= - \frac{1}{2 y - x} - 0

Simplify

= - \frac{1}{2 y - x}

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What is (\partial)/(\partial x)(sqrt(y-x)-z) ?
The answer to (\partial)/(\partial x)(sqrt(y-x)-z) is -1/(2sqrt(y-x))