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

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

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

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

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derivative of

\frac{x ^{2}}{x ^{2} + 3}

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

Solution steps

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

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

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

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

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

Simplify

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

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

y^{^{'}} = x^{2} y - y + x^{2} - 1

\int e [2 x] d x

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

\int_{0.1}^{1} 1.5 x^{2} d x

x \to 4 lim (\frac{x}{- 7 x + 1})

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