What is the d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) ?

The d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) is ({x}}{{y)/z}

What is the first d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) ?

The first d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) is ({x}}{{y)/z}

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

\frac{x}{y z}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{\frac{x y}{z}} \frac{d}{d y} (\frac{x y}{z})

= \frac{1}{\frac{x y}{z}} \frac{d}{d y} (\frac{x y}{z})

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

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

Simplify

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

= \frac{x}{y z}

d er i v a t i v e 12 x - 2 x

\int - \frac{1}{k} cos (k x) d x

\frac{\partial}{\partial y} (6 y e^{2 x y} + x)

x \to 0 - lim (\frac{x}{∣ x ∣})

\int_{1}^{2} \frac{5 x ^{2} - 1}{x} d x

What is the d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) ?
The d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) is ({x}}{{y)/z}
What is the first d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) ?
The first d/(d{y)}(({x}ln(({x)/y)/({z)})}{{z}}) is ({x}}{{y)/z}