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

The derivative of (e^x(x-2))/((x-1)^2) is (e^x(x^2-4x+5))/((x-1)^3)

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

The first derivative of (e^x(x-2))/((x-1)^2) is (e^x(x^2-4x+5))/((x-1)^3)

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derivative of

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

\frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( x - 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( e ^{x} x - e ^{x} ) ( x - 1 ) ^{2} - 2 ( x - 1 ) e ^{x} ( x - 2 )}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( x - 1 ) ^{3}}

= \frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( x - 1 ) ^{3}}

\int \frac{1}{x ^{2} + 9 x + 18} d x

\int sin (θ) + 1 d θ

\int cosh (5 x) d x

t a y l or x, 1

\int_{7}^{11} \frac{2}{x ^{3}} d x

What is the derivative of (e^x(x-2))/((x-1)^2) ?
The derivative of (e^x(x-2))/((x-1)^2) is (e^x(x^2-4x+5))/((x-1)^3)
What is the first derivative of (e^x(x-2))/((x-1)^2) ?
The first derivative of (e^x(x-2))/((x-1)^2) is (e^x(x^2-4x+5))/((x-1)^3)