2.4 Lösning 4c
Från Mathonline
\[ y = {2 \over 3}\,x\,\sqrt{x} - {1 \over x^2} = {2 \over 3}\,x\cdot x^{1 \over 2} - {1 \over x^2} = {2 \over 3}\, x^{1+{1 \over 2}} - {1 \over x^2} = {2 \over 3}\, x^{3 \over 2} - {1 \over x^2} = {2 \over 3}\, x^{3 \over 2} - x^{-2} \]
\[ y\,' = {3 \over 2}\cdot {2 \over 3}\, x^{{3 \over 2}-1} - (-2)\cdot x^{-2-1} = x^{1 \over 2} + 2\cdot x^{-3} = \sqrt{x} + 2\cdot {1 \over x^3} = \sqrt{x} + {2 \over x^3}\]
