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}

\frac{d}{d x} (\frac{3 x - 4}{( 5 x + 2 ) ^{3}})

\int_{0}^{3} \frac{1}{36 - x ^{2}} d x

f (x) = (6 x + 2)^{3}

\int - \frac{x}{x - 1} d x

y = 13 + 2 x - x^{2}, y = 3 x + 1

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