Найдите производную функции \(\large{y=5^{\frac{x}{2}}{\tg{4x}}.}\) \(\large{y'=0,5\cdot5^{\frac{x}{2}}{\ln5}\cdot{\tg{4x}}+\dfrac{4\cdot5^{\frac{x}{2}}}{\cos^2{4x}}.}\) \(\large{y'=0,5\cdot5^{\frac{x}{2}}\cdot\dfrac{1}{\cos^2{4x}}}\) \(\large{y'=5^{\frac{x}{2}}{\tg{4x}}+{\Large\frac{5^{\frac{x}{2}}}{\cos^2{4x}}}}\) \(\Large{y'=\frac{5^{\frac{x}{2}}{\ln5}}{\cos^2{4x}}.}\)

Задание

Найдите производную функции \(\large{y=5^{\frac{x}{2}}{\tg{4x}}.}\)

\(\large{y'=0,5\cdot5^{\frac{x}{2}}{\ln5}\cdot{\tg{4x}}+\dfrac{4\cdot5^{\frac{x}{2}}}{\cos^2{4x}}.}\)
\(\large{y'=0,5\cdot5^{\frac{x}{2}}\cdot\dfrac{1}{\cos^2{4x}}}\)
\(\large{y'=5^{\frac{x}{2}}{\tg{4x}}+{\Large\frac{5^{\frac{x}{2}}}{\cos^2{4x}}}}\)
\(\Large{y'=\frac{5^{\frac{x}{2}}{\ln5}}{\cos^2{4x}}.}\)