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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derivative of

\frac{e ^{x}}{x}

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

Solution steps

\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}}

\int_{1}^{2} x ln (x) d x

x \frac{d y}{d x} + (2 x + 1) y = x e^{- 2 x}

\int \frac{x ^{2}}{x - 2} d x

\int (e^{x} + 1)^{3} e^{x} d x

\int e^{i 8 x} cos (5 x) d x

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)