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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

3 ln (5 x)

x^{2} + 2 x y + x \frac{d y}{d x} = 0

3 x^{4} - 65 x^{3}

\int 2 sec^{4} (x) d x

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