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

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

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

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

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derivative of

f (x) = \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}}

x \to - 3 lim (\frac{x ^{3} + 8}{x + 2})

e^{2 - 5 x}

x \to 0 lim (\frac{3 - 7 x}{2 x})

x^{2} e^{- x}

\int cos (e^{x}) d x

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