TeX Quellcode:

\begin{array}{ccllrcl}\quad\mathbb{D} &=& \mathbb{R}\\\quad a &\in& \mathbb{R}\\\\f(x) &=& ax^2\cdot 5^3\sin(x)+17ax^3\\&=& 125ax^2\cdot\sin(x)+17ax^3\\\\\quad u(x) &=& 125ax^2 &\Rightarrow & u'(x) &=& 250ax\\\quad v(x) &=& \sin(x) &\Rightarrow & v'(x) &=& \cos(x)\\\\f'(x) &=& 250ax\cdot \sin(x)+125ax^2\cdot\cos(x)+51ax^2\\&=& ax\left(250\sin(x)+125x\cdot\cos(x)+51x\right)\\\end{array}