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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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

y^{^{'}} = 2 e^{2 x - y}, y (0) = 0

\frac{d}{d x} (x^{3} - x^{2} + 7 x - 1)

\int 2 \cdot cos (x) d x

h \to 0 lim (\frac{cos ( h ) - 1}{h})

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