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

The derivative of ((x^2)/(x^2+4)) is (8x)/((x^2+4)^2)

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

The first derivative of ((x^2)/(x^2+4)) is (8x)/((x^2+4)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 x ( x ^{2} + 4 ) - 2 x x ^{2}}{( x ^{2} + 4 ) ^{2}} : \frac{8 x}{( x ^{2} + 4 ) ^{2}}

= \frac{8 x}{( x ^{2} + 4 ) ^{2}}

What is the derivative of ((x^2)/(x^2+4)) ?
The derivative of ((x^2)/(x^2+4)) is (8x)/((x^2+4)^2)
What is the first derivative of ((x^2)/(x^2+4)) ?
The first derivative of ((x^2)/(x^2+4)) is (8x)/((x^2+4)^2)