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

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

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

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

\frac{1}{2 y - x}

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

f (x) = 5 - 3 (1 + x^{2})^{- 1}

x \to 1 lim (\frac{2 x ^{3} - 14 x ^{2} + 12 x}{x ^{3} - 10 x ^{2} + 27 x - 18})

x \cdot \frac{d y}{d x} + y = y^{2} x^{2} ln (x)

cos (a^{6} + x^{6})

\frac{d}{d x} (ln (b - a x))

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