What is the derivative of sqrt(x*y) ?

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

What is the first derivative of sqrt(x*y) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x y} (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(x*y) ?
The derivative of sqrt(x*y) is (y+x\frac{dy)/(dx)}{2sqrt(xy)}
What is the first derivative of sqrt(x*y) ?
The first derivative of sqrt(x*y) is (y+x\frac{dy)/(dx)}{2sqrt(xy)}