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Popular >

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

Solution

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

Solution

\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}}

Popular Examples

integral of (2x)/(sqrt(9-4x^2))

\int \frac{2 x}{9 - 4 x ^{2}} d x

derivative of 2-2sin(x)

\frac{d}{d x} (2 - 2 sin (x))

integral from 1 to 4 of (4x^2)

\int_{1}^{4} (4 x^{2}) d x

x^2y^{''}-5xy^'+9y=0,y(1)=-5,y^'(1)=-17

x^{2} y^{^{''}} - 5 x y^{^{'}} + 9 y = 0, y (1) = - 5, y^{^{'}} (1) = - 17

slope of (-3.1)(0.3)slope

(- 3.1) (0.3)

Frequently Asked Questions (FAQ)

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)