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

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

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(\partial)/(\partial x)(zln|x|)

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

\frac{z}{x}

Solution steps

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

Treat

z

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{z}{x}

(6 y + 2 t - 7) d t + (4 y + 6 t - 1) d y = 0, y (- 1) = 2

\frac{d y}{d x}, y = 3^{x}

\frac{d}{d x} (\frac{1}{x ^{\frac{3}{4}}})

x \to 3 lim (x)

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

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