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

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

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

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

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

\frac{2 ( - 3 x ^{3} + 3 x ^{2} + 9 x - 1 )}{( x ^{2} + 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (3 x^{2} - 2 x - 3) = 6 x - 2

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

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

Simplify

\frac{( 6 x - 2 ) ( x ^{2} + 1 ) ^{2} - 4 x ( x ^{2} + 1 ) ( 3 x ^{2} - 2 x - 3 )}{( ( x ^{2} + 1 ) ^{2} ) ^{2}} : \frac{2 ( - 3 x ^{3} + 3 x ^{2} + 9 x - 1 )}{( x ^{2} + 1 ) ^{3}}

= \frac{2 ( - 3 x ^{3} + 3 x ^{2} + 9 x - 1 )}{( x ^{2} + 1 ) ^{3}}

y^{^{'}} = x - x y

\int e^{s i n (t)} d t

(1.1) (4.2)

\frac{2}{[ ( 4 s ^{2} - 8 s ) ]}

\int \frac{36 - x ^{2}}{x} d x

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