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

The derivative of-(2x/((3+x^2)^2)) is -(6(-x^2+1))/((3+x^2)^3)

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

The first derivative of-(2x/((3+x^2)^2)) is -(6(-x^2+1))/((3+x^2)^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 + x^{2})^{2}) = 4 x (3 + x^{2})

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

Simplify

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

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

\int (\frac{2 x + y + z}{( x + y ) ( x + z )}) d x

x^{4} cos (x^{3})

\frac{\partial}{\partial x} (4 cos (x^{2} + y^{2}))

e^{t} cos (6 t)

5 - x^{2}

What is the derivative of-(2x/((3+x^2)^2)) ?
The derivative of-(2x/((3+x^2)^2)) is -(6(-x^2+1))/((3+x^2)^3)
What is the first derivative of-(2x/((3+x^2)^2)) ?
The first derivative of-(2x/((3+x^2)^2)) is -(6(-x^2+1))/((3+x^2)^3)