TeX Quellcode:

\begin{array}{rcl}f'_x(x,y,z) &=& \dfrac{3}{2}\cdot 2x^{2-1}y^{\frac{1}{2}}z^3+4\cdot\dfrac{1}{3}x^{\frac{1}{3}-1}y^2\\\\&=& 3x^1y^{\frac{1}{2}}z^3+\dfrac{4}{3}x^{-\frac{2}{3}}y^2\\\\&=& 3x\sqrt{y}z^3+\dfrac{4y^2}{3x^{\frac{2}{3}}}\end{array}