4. Pochodna funkcji złożonej:

 $[f\left(g\left(x\right)\right){]}^{\prime }=f^{\prime }\left(g\left(x\right)\right)\cdot g^{\prime }\left(x\right)$

$p\left(x\right)=\ln \left(2x^3\right)$

$p^{\prime }\left(x\right)={\left(\ln \left(2x^3\right)\right)}^{\prime }=$

${={\ln }^{\prime }\left(2x^3\right)\cdot \left(2x^3\right)}^{\prime }=$

$=\frac{1}{2x^3}\cdot {\left(2x^3\right)}^{\prime }=$

$=\frac{1}{2x^3}\cdot 2\cdot {\left(x^3\right)}^{{}^{\prime }}=$

$=\frac{1}{\cancel{2}{x}^3}\cdot \cancel{2}\cdot \left(3x^2\right)=$

$=\frac{1}{x^{{\cancel{3}}^1}}\cdot 3\cancel{x^2}=\frac{3}{x}$