What is the derivative of sqrt(2xy) ?

The derivative of sqrt(2xy) is (y+x\frac{dy)/(dx)}{sqrt(2)sqrt(xy)}

What is the first derivative of sqrt(2xy) ?

The first derivative of sqrt(2xy) is (y+x\frac{dy)/(dx)}{sqrt(2)sqrt(xy)}

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

\frac{y + x \frac{d y}{d x}}{2 x y}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 2 x y} \cdot 2 (y + x \frac{d y}{d x})

Simplify

\frac{1}{2 2 x y} \cdot 2 (y + x \frac{d y}{d x}) : \frac{y + x \frac{d y}{d x}}{2 x y}

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

What is the derivative of sqrt(2xy) ?
The derivative of sqrt(2xy) is (y+x\frac{dy)/(dx)}{sqrt(2)sqrt(xy)}
What is the first derivative of sqrt(2xy) ?
The first derivative of sqrt(2xy) is (y+x\frac{dy)/(dx)}{sqrt(2)sqrt(xy)}