What is the derivative of (2e^x/(5x)) ?

The derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)

What is the first derivative of (2e^x/(5x)) ?

The first derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)

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\frac{d}{d x} (\frac{2 e ^{x}}{5 x})

\frac{2 ( e ^{x} x - e ^{x} )}{5 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 e ^{x}}{5 x})

Take the constant out:

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

= \frac{2}{5} \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{2}{5} \cdot \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{2}{5} \cdot \frac{e ^{x} x - 1 \cdot e ^{x}}{x ^{2}}

Simplify

\frac{2}{5} \cdot \frac{e ^{x} x - 1 \cdot e ^{x}}{x ^{2}} : \frac{2 ( e ^{x} x - e ^{x} )}{5 x ^{2}}

= \frac{2 ( e ^{x} x - e ^{x} )}{5 x ^{2}}

What is the derivative of (2e^x/(5x)) ?
The derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)
What is the first derivative of (2e^x/(5x)) ?
The first derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)