Rozwiązanie:
[tex]i)[/tex]
[tex]$y=\sin \Big(\ln (1+x^{4})\Big)[/tex]
[tex]$y'=\cos \Big(\ln (1+x^{4})\Big) \cdot \frac{4x^{3}}{1+x^{4}} =\frac{4x^{3}\cos \Big(\ln (1+x^{4})\Big)}{1+x^{4}}[/tex]
[tex]h)[/tex]
[tex]y=x \ln (x^{2}+1)[/tex]
[tex]$y'=\ln(x^{2}+1)+\frac{2x^{2}}{x^{2}+1}[/tex]
[tex]l)[/tex]
[tex]$y=\frac{xe^{x^{2}}}{\ln(x^{2})}[/tex]
[tex]$y'=\frac{\Big(e^{x^{2}}+2x^{2}e^{x^{2}}\Big)\ln(x^{2})-\frac{2x}{x^{2}}\cdot xe^{x^{2}} }{\ln^{2}(x^{2})}=\frac{\Big(e^{x^{2}}+2x^{2}e^{x^{2}}\Big)\ln(x^{2})-2e^{x^{2}} }{\ln^{2}(x^{2})}[/tex]
