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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\frac{d}{d x} (- \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}}

\frac{\partial}{\partial x} (x^{a} y^{b} z^{c})

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

\frac{d}{d x} (ln (e^{7 x}))

x \to - 3 lim (- 1)

\int \frac{1}{( x + 4 ) x ^{2} + 8 x} d x

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)