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

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

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

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

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derivative of

- \frac{2 x}{( 4 + x ^{2} ) ^{2}}

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

x^{3} - 6 x^{2} - 34 x + 40, at x = 4

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

\frac{\partial}{\partial z} (\frac{x y}{x + y + z})

\frac{d}{d x} (\frac{cos ( x )}{4 x})

x \to 1 - lim (x^{3} - 4)

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