What is the derivative of (32x/((x^2+3)^2)) ?

The derivative of (32x/((x^2+3)^2)) is (96(-x^2+1))/((x^2+3)^3)

What is the first derivative of (32x/((x^2+3)^2)) ?

The first derivative of (32x/((x^2+3)^2)) is (96(-x^2+1))/((x^2+3)^3)

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\frac{d}{d x} (\frac{32 x}{( x ^{2} + 3 ) ^{2}})

\frac{96 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{32 x}{( x ^{2} + 3 ) ^{2}})

Take the constant out:

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

= 32 \frac{d}{d x} (\frac{x}{( x ^{2} + 3 ) ^{2}})

Apply the Quotient Rule:

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

= 32 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 3 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 3 ) ^{2} ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}}

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

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

= 32 \cdot \frac{1 \cdot ( x ^{2} + 3 ) ^{2} - 4 x ( x ^{2} + 3 ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}}

Simplify

32 \cdot \frac{1 \cdot ( x ^{2} + 3 ) ^{2} - 4 x ( x ^{2} + 3 ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}} : \frac{96 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

= \frac{96 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

4 t^{- \frac{3}{8}}

\int \frac{( x + 7 ) ^{7}}{2 x} d x

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

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

\int 3 e^{5 x} - 3 cos (4 x) d x

What is the derivative of (32x/((x^2+3)^2)) ?
The derivative of (32x/((x^2+3)^2)) is (96(-x^2+1))/((x^2+3)^3)
What is the first derivative of (32x/((x^2+3)^2)) ?
The first derivative of (32x/((x^2+3)^2)) is (96(-x^2+1))/((x^2+3)^3)