What is the derivative of f(x)=(x^3)/((x^2+4)^2) ?

The derivative of f(x)=(x^3)/((x^2+4)^2) is (x^2(-x^2+12))/((x^2+4)^3)

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

The first derivative of f(x)=(x^3)/((x^2+4)^2) is (x^2(-x^2+12))/((x^2+4)^3)

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derivative of

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

\frac{x ^{2} ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{3 x ^{2} ( x ^{2} + 4 ) ^{2} - 4 x ( x ^{2} + 4 ) x ^{3}}{( ( x ^{2} + 4 ) ^{2} ) ^{2}} : \frac{x ^{2} ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

= \frac{x ^{2} ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

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

\frac{d}{d x} (- \frac{3}{4} x^{\frac{1}{3}})

y^{^{'}} - \frac{3 y}{x} = x

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

\frac{\partial}{\partial x} (\frac{2}{x + 2 y})

What is the derivative of f(x)=(x^3)/((x^2+4)^2) ?
The derivative of f(x)=(x^3)/((x^2+4)^2) is (x^2(-x^2+12))/((x^2+4)^3)
What is the first derivative of f(x)=(x^3)/((x^2+4)^2) ?
The first derivative of f(x)=(x^3)/((x^2+4)^2) is (x^2(-x^2+12))/((x^2+4)^3)