TeX source:
\begin{array}{lclcrcl}\quad\mathbb{D}&=&\mathbb{R} \cr \cr f(x) &=& x \cdot e^{-5x^2} \cr\cr \quad u(x) &=& x & \Rightarrow & u'(x) &=& 1 \cr \quad v(h(x)) &=& e^{h(x)} & \Rightarrow & v'(h(x)) &=& e^{h(x)} \cr \quad h(x) &=& -5x^2 & \Rightarrow & h'(x) &=& -10x \cr\cr f'(x) &=& 1 \cdot e^{-5x^2} + x\cdot e^{-5x^2} \cdot \left( -10x \right) \cr &=& e^{-5x^2} - 10x^2 \cdot e^{-5x^2} \cr &=& e^{-5x^2} \cdot \left(1 - 10x^2\right) \end{array}