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

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

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

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

\frac{1}{2 y - x}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{x ^{2}}{9}

\int_{0}^{1} \frac{x}{x ^{2} + 1} d x

\frac{d}{d x} (1 + 2 sin (\frac{x ^{2}}{2}))

\int \frac{4}{x ^{2} + 16} d x

\int \frac{2 ( x + 2 )}{5} d x

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