What is (\partial)/(\partial x)(sqrt(2xy)) ?

The answer to (\partial)/(\partial x)(sqrt(2xy)) is (sqrt(y))/(sqrt(2)\sqrt{x)}

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(\partial)/(\partial x)(sqrt(2xy))

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

\frac{y}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 2 x y} \cdot 2 y : \frac{y}{2 x}

= \frac{y}{2 x}

f (x) = (9 - 6 x^{2})^{2}

(2 x + y + 1) y^{^{'}} = 1

(x^{2} - 1)^{^{'}}

\frac{d}{d x} f (x) = - 9

\frac{d}{d x} (\frac{x}{3 x ^{2} + 1})

What is (\partial)/(\partial x)(sqrt(2xy)) ?
The answer to (\partial)/(\partial x)(sqrt(2xy)) is (sqrt(y))/(sqrt(2)\sqrt{x)}