What is the derivative of (xy)^{1/2} ?

The derivative of (xy)^{1/2} is 1/(2(xy)^{1/2)}y

What is the first derivative of (xy)^{1/2} ?

The first derivative of (xy)^{1/2} is 1/(2(xy)^{1/2)}y

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derivative of

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

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What is the derivative of (xy)^{1/2} ?
The derivative of (xy)^{1/2} is 1/(2(xy)^{1/2)}y
What is the first derivative of (xy)^{1/2} ?
The first derivative of (xy)^{1/2} is 1/(2(xy)^{1/2)}y