Ответ:

[tex]\dfrac{24\sqrt{x^{5}}}{\cos^{2}x}+60tgx\sqrt{x^{3}}[/tex]

Пошаговое объяснение:

[tex]y=4tgx \cdot 6\sqrt{x^{5}}=24tgx \cdot x^{\tfrac{5}{2}};[/tex]

[tex]y'=(24tgx \cdot x^{\tfrac{5}{2}})=24 \cdot (tgx \cdot x^{\tfrac{5}{2}})'=24 \cdot ((tgx)' \cdot x^{\tfrac{5}{2}}+tgx \cdot (x^{\tfrac{5}{2}})')=[/tex]

[tex]=24 \cdot \bigg (\dfrac{1}{\cos^{2}x} \cdot \sqrt{x^{5}}+tgx \cdot \dfrac{5}{2} \cdot x^{\tfrac{5}{2}-1} \bigg )=24 \cdot \bigg (\dfrac{\sqrt{x^{5}}}{\cos^{2}x}+\dfrac{5}{2}tgx \cdot x^{\tfrac{3}{2}} \bigg )=[/tex]

[tex]=\dfrac{24\sqrt{x^{5}}}{\cos^{2}x}+60tgx\sqrt{x^{3}} \ ;[/tex]