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

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

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

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

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

\int (sec^{2} (x) + x) d x

\int_{b}^{a} f (x) d x

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

x \to 0 lim (e^{x^{2}})

\int_{1}^{2} x^{3} ln (x) d x

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