Źródło TeX:

f^\prime(x)=\left(\frac{x^2}{x^2+3}\right)^\prime=\frac{\left(x^2\right)^\prime\cdot \left(x^2+3\right)+x^2\cdot\left(x^2+3\right)^\prime}{\left(x^2+3\right)^2}=\frac{2x\cdot\left(x^2+3\right)-x^2\cdot 2x}{\left(x^2+3\right)^2}=\frac{6x}{\left(x^2+3\right)^2}, \; \; x\in\mathbb R