What is (\partial)/(\partial x)(Asqrt(x/z)) ?

The answer to (\partial)/(\partial x)(Asqrt(x/z)) is A/(2sqrt(x)\sqrt{z)}

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(\partial)/(\partial x)(Asqrt(x/z))

\frac{\partial}{\partial x} (A \frac{x}{z})

\frac{A}{2 x z}

Solution steps

\frac{\partial}{\partial x} (A \frac{x}{z})

Treat

A, z

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= A \frac{\partial}{\partial x} (\frac{x}{z})

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x}{z}) = \frac{1}{z}

= A \frac{1}{2 \frac{x}{z}} \cdot \frac{1}{z}

Simplify

A \frac{1}{2 \frac{x}{z}} \cdot \frac{1}{z} : \frac{A}{2 x z}

= \frac{A}{2 x z}

What is (\partial)/(\partial x)(Asqrt(x/z)) ?
The answer to (\partial)/(\partial x)(Asqrt(x/z)) is A/(2sqrt(x)\sqrt{z)}