What is (\partial)/(\partial x)(zln(xy)) ?

The answer to (\partial)/(\partial x)(zln(xy)) is z/x

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(\partial)/(\partial x)(zln(xy))

\frac{\partial}{\partial x} (z ln (x y))

\frac{z}{x}

Solution steps

\frac{\partial}{\partial x} (z ln (x y))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (ln (x y))

Apply the chain rule:

\frac{1}{x y} \frac{\partial}{\partial x} (x y)

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

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

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

Simplify

z \frac{1}{x y} y : \frac{z}{x}

= \frac{z}{x}

\frac{s + 2}{( s + 1 ) ( s - s ^{2} )}

\int \frac{8 x ^{2} - 4 x + 7}{4 x ^{3} + x ^{2} + 4 x + 1} d x

f (x) = - x^{2} - 4 x + 2, at x = - 1

\frac{d}{d x} (\frac{x ^{2} - 36}{x + 6})

\frac{d}{d x} (3^{x + 10})

What is (\partial)/(\partial x)(zln(xy)) ?
The answer to (\partial)/(\partial x)(zln(xy)) is z/x