What is the derivative of-(e^x/x) ?

The derivative of-(e^x/x) is -(e^xx-e^x)/(x^2)

What is the first derivative of-(e^x/x) ?

The first derivative of-(e^x/x) is -(e^xx-e^x)/(x^2)

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\frac{d}{d x} (- \frac{e ^{x}}{x})

- \frac{e ^{x} x - e ^{x}}{x ^{2}}

Solution steps

\frac{d}{d x} (- \frac{e ^{x}}{x})

Take the constant out:

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

= - \frac{d}{d x} (\frac{e ^{x}}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (e^{x}) = e^{x}

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

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

Simplify

= - \frac{e ^{x} x - e ^{x}}{x ^{2}}

What is the derivative of-(e^x/x) ?
The derivative of-(e^x/x) is -(e^xx-e^x)/(x^2)
What is the first derivative of-(e^x/x) ?
The first derivative of-(e^x/x) is -(e^xx-e^x)/(x^2)