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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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