TeX source:
\begin{array}{cclcrcl}\quad\mathbb{D} &=& \mathbb{R} \\\\f(x) &=& 5{,}5^x\cdot x^5-5 \\\\\quad u(x) &=& 5{,}5^x &\Rightarrow & u'(x) &=& 5{,}5^x\cdot\ln(5{,}5) \\\quad v(x) &=& x^5 &\Rightarrow & v'(x) &=& 5x^4 \\\\f'(x) &=& 5{,}5^x\cdot\ln(5{,}5)\cdot x^5+5{,}5^x\cdot 5x^4 \\&=& 5{,}5^x x^4\left(x\ln(5{,}5)+5\right)\end{array}