What is the derivative of (2x^2-13x+20/((x-1)^2)) ?

The derivative of (2x^2-13x+20/((x-1)^2)) is (9(x-3))/((x-1)^3)

What is the first derivative of (2x^2-13x+20/((x-1)^2)) ?

The first derivative of (2x^2-13x+20/((x-1)^2)) is (9(x-3))/((x-1)^3)

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\frac{d}{d x} (\frac{2 x ^{2} - 13 x + 20}{( x - 1 ) ^{2}})

\frac{9 ( x - 3 )}{( x - 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{2} - 13 x + 20}{( x - 1 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} - 13 x + 20 ) ( x - 1 ) ^{2} - \frac{d}{d x} ( ( x - 1 ) ^{2} ) ( 2 x ^{2} - 13 x + 20 )}{( ( x - 1 ) ^{2} ) ^{2}}

\frac{d}{d x} (2 x^{2} - 13 x + 20) = 4 x - 13

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

= \frac{( 4 x - 13 ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( 2 x ^{2} - 13 x + 20 )}{( ( x - 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 4 x - 13 ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( 2 x ^{2} - 13 x + 20 )}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{9 ( x - 3 )}{( x - 1 ) ^{3}}

= \frac{9 ( x - 3 )}{( x - 1 ) ^{3}}

\int x^{3} x^{2} + 42 d x

x \to 1 lim (\frac{x ^{2} + x}{x - 1})

6 t \frac{d y}{d t} + y = t^{5}

\frac{d}{d x} (1 + cos^{2} (x))

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

What is the derivative of (2x^2-13x+20/((x-1)^2)) ?
The derivative of (2x^2-13x+20/((x-1)^2)) is (9(x-3))/((x-1)^3)
What is the first derivative of (2x^2-13x+20/((x-1)^2)) ?
The first derivative of (2x^2-13x+20/((x-1)^2)) is (9(x-3))/((x-1)^3)