What is the derivative of (e^{x-2})/(x-1) ?

The derivative of (e^{x-2})/(x-1) is (e^{x-2}x-2e^{x-2})/((x-1)^2)

What is the first derivative of (e^{x-2})/(x-1) ?

The first derivative of (e^{x-2})/(x-1) is (e^{x-2}x-2e^{x-2})/((x-1)^2)

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derivative of

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

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

Solution steps

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

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

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

\frac{d}{d x} (x - 1) = 1

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

Simplify

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

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

n = 0 \sum \infty \frac{1}{( 2 n ) !}

\frac{d}{d x} (arctan (x^{2} + 2 x) + C)

\int \frac{x}{1 + 5 x ^{2}} d x

y = 3 x^{2} + \frac{1}{x}

What is the derivative of (e^{x-2})/(x-1) ?
The derivative of (e^{x-2})/(x-1) is (e^{x-2}x-2e^{x-2})/((x-1)^2)
What is the first derivative of (e^{x-2})/(x-1) ?
The first derivative of (e^{x-2})/(x-1) is (e^{x-2}x-2e^{x-2})/((x-1)^2)