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

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (2 x^{3} - 5 x^{2} + 4 x) = 6 x^{2} - 10 x + 4

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

= \frac{( 6 x ^{2} - 10 x + 4 ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( 2 x ^{3} - 5 x ^{2} + 4 x )}{( ( x - 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 6 x ^{2} - 10 x + 4 ) ( x - 1 ) ^{2} - 2 ( x - 1 ) ( 2 x ^{3} - 5 x ^{2} + 4 x )}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{2 ( x ^{3} - 3 x ^{2} + 3 x - 2 )}{( x - 1 ) ^{3}}

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

\int (- 2) x d x

\int_{0}^{1} x^{2} 6 x + 8 d x

\int \frac{( 7 x ^{2} + 5 x + 7 )}{( x ^{2} + 1 ) ^{2}} d x

\frac{d}{d x} (\frac{16}{x ^{2}} - \frac{4}{x})

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