What is the derivative of (e^{x-3}/(x-2)) ?

The derivative of (e^{x-3}/(x-2)) is (e^{x-3}x-3e^{x-3})/((x-2)^2)

What is the first derivative of (e^{x-3}/(x-2)) ?

The first derivative of (e^{x-3}/(x-2)) is (e^{x-3}x-3e^{x-3})/((x-2)^2)

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\frac{d}{d x} (\frac{e ^{x - 3}}{x - 2})

\frac{e ^{x - 3} x - 3 e ^{x - 3}}{( x - 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x - 3}}{x - 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x - 3} ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) e ^{x - 3}}{( x - 2 ) ^{2}}

\frac{d}{d x} (e^{x - 3}) = e^{x - 3}

\frac{d}{d x} (x - 2) = 1

= \frac{e ^{x - 3} ( x - 2 ) - 1 \cdot e ^{x - 3}}{( x - 2 ) ^{2}}

Simplify

\frac{e ^{x - 3} ( x - 2 ) - 1 \cdot e ^{x - 3}}{( x - 2 ) ^{2}} : \frac{e ^{x - 3} x - 3 e ^{x - 3}}{( x - 2 ) ^{2}}

= \frac{e ^{x - 3} x - 3 e ^{x - 3}}{( x - 2 ) ^{2}}

x \to - 4 lim (m (x) (3 x + 2) + 2 k)

\int_{5}^{20} (x^{2} x) d x

x \to 0 lim (\frac{5 x}{sin ( x )})

\frac{d}{d x} (lo g_{10} (cos (x)))

n = 0 \sum \infty n^{3} (x - 5)^{n}

What is the derivative of (e^{x-3}/(x-2)) ?
The derivative of (e^{x-3}/(x-2)) is (e^{x-3}x-3e^{x-3})/((x-2)^2)
What is the first derivative of (e^{x-3}/(x-2)) ?
The first derivative of (e^{x-3}/(x-2)) is (e^{x-3}x-3e^{x-3})/((x-2)^2)