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

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

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

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

\frac{1}{2 x - y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d}{d x} (2 x e^{6 x} + e^{6 x} \cdot 6 x^{2})

\int 2 x^{2} sin (x) d x

\frac{d}{d x} ((x^{2} + x^{3})^{4})

\int 3 tan^{2} (x) sec^{3} (x) d x

\frac{d}{d x} (ln x^{2} + 9)

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