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

The d/(d{z)}(({x}ln(({x)/y)/({z)})}{{z}}) is ((-1-ln(({x)/y)/({z)})){x}}{{z}^2}

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

The first d/(d{z)}(({x}ln(({x)/y)/({z)})}{{z}}) is ((-1-ln(({x)/y)/({z)})){x}}{{z}^2}

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Popular >

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

\frac{( - 1 - ln ( \frac{x y}{z} ) ) x}{z ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= x \frac{\frac{d}{d z} ( ln ( \frac{x y}{z} ) ) z - \frac{d}{d z} ( z ) ln ( \frac{x y}{z} )}{z ^{2}}

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

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

= x \frac{( - \frac{1}{z} ) z - 1 \cdot ln ( \frac{x y}{z} )}{z ^{2}}

Simplify

x \frac{( - \frac{1}{z} ) z - 1 \cdot ln ( \frac{x y}{z} )}{z ^{2}} : \frac{( - 1 - ln ( \frac{x y}{z} ) ) x}{z ^{2}}

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

\frac{d}{d x} (3 x + 7 x)

\frac{z}{z + \frac{a}{z}}

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

y = 2 x^{3} + 3 x^{2} - 12 x + 3

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

What is the d/(d{z)}(({x}ln(({x)/y)/({z)})}{{z}}) ?
The d/(d{z)}(({x}ln(({x)/y)/({z)})}{{z}}) is ((-1-ln(({x)/y)/({z)})){x}}{{z}^2}
What is the first d/(d{z)}(({x}ln(({x)/y)/({z)})}{{z}}) ?
The first d/(d{z)}(({x}ln(({x)/y)/({z)})}{{z}}) is ((-1-ln(({x)/y)/({z)})){x}}{{z}^2}