What is the derivative of (e^{x-2}/x) ?

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

What is the first derivative of (e^{x-2}/x) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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