What is the derivative of e^{|x|} ?

The derivative of e^{|x|} is (e^{|x|}x)/(|x|)

What is the first derivative of e^{|x|} ?

The first derivative of e^{|x|} is (e^{|x|}x)/(|x|)

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\frac{d}{d x} (e^{∣ x ∣})

\frac{e ^{∣ x ∣} x}{∣ x ∣}

Solution steps

\frac{d}{d x} (e^{∣ x ∣})

Apply the chain rule:

e^{∣ x ∣} \frac{d}{d x} (∣ x ∣)

= e^{∣ x ∣} \frac{d}{d x} (∣ x ∣)

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

= e^{∣ x ∣} \frac{x}{∣ x ∣}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{∣ x ∣} x}{∣ x ∣}

\frac{\partial}{\partial x} (cos (x + 2 y))

y = (x^{3} - 9 x)^{8}, (3, 0)

x^{2} y^{^{''}} - 2 x y^{^{'}} + 2 y = x^{2} + 2

\frac{d}{d x} (\frac{0.9 e ^{x}}{tan ( x )})

(x^{\frac{1}{3}})^{^{'}}

What is the derivative of e^{|x|} ?
The derivative of e^{|x|} is (e^{|x|}x)/(|x|)
What is the first derivative of e^{|x|} ?
The first derivative of e^{|x|} is (e^{|x|}x)/(|x|)