What is the derivative of sqrt(xy) ?

The derivative of sqrt(xy) is 1/(2sqrt(xy))y

What is the first derivative of sqrt(xy) ?

The first derivative of sqrt(xy) is 1/(2sqrt(xy))y

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derivative of

x y

\frac{1}{2 x y} y

Solution steps

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

Treat

y

as a constant

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

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

What is the derivative of sqrt(xy) ?
The derivative of sqrt(xy) is 1/(2sqrt(xy))y
What is the first derivative of sqrt(xy) ?
The first derivative of sqrt(xy) is 1/(2sqrt(xy))y