What is the first derivative of (|x|/x) ?

The first derivative of (|x|/x) is 0

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derivative of (|x|/x)

\frac{d}{d x} (\frac{∣ x ∣}{x})

0

Solution steps

\frac{d}{d x} (\frac{∣ x ∣}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ∣ x ∣ ) x - \frac{d x}{d x} ∣ x ∣}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{\frac{x}{∣ x ∣} x - 1 \cdot ∣ x ∣}{x ^{2}}

Simplify

\frac{\frac{x}{∣ x ∣} x - 1 \cdot ∣ x ∣}{x ^{2}} : 0

= 0

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

x y^{^{'}} + y = - 2 x y^{2}, y (1) = - 5

\frac{d}{d x} (tanh (x))

\int \frac{1}{3 - 5 x} d x

7 x - x^{2} (1.6)