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

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

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

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

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derivative of

f (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}}

\int \frac{1}{z ^{2} - z} d z

\int_{1}^{7} \frac{1}{9 + ( x + 2 ) ^{2}} d x

\int (2 x^{3} - 3 x + 5) d x

\int x cot (x^{2}) d x

y^{^{'}} + y = e^{- t}

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