Y=arccos√1-e^2x. Найти производные

Решите задачу:

$y=arccos(\sqrt{1-e^{2x}})\\\\y=f(g(h(u(x)))):\\f(t)=arccos(t)\\g(s)=\sqrt{s}\\h(q)=1-e^q\\u(x)=2x\\\\y'=f'(g(h(u(x))))*g'(h(u(x)))*h'(u(x))*u'(x)\\\\f'(t)=-\frac{1}{\sqrt{1-t^2}}\\g'(s)=\frac{1}{2\sqrt{s}}\\h'(q)=-e^q\\u'(x)=2$

$y'=(-\frac{1}{\sqrt{1-(\sqrt{1-e^{2x}})^2}})(\frac{1}{2\sqrt{1-e^{2x}}})(-e^{2x})(2)=\\\\\frac{2e^{2x}}{2\sqrt{1-e^{2x}}}(\frac{1}{\sqrt{1-(1-e^{2x})}})=\frac{e^{2x}}{\sqrt{1-e^{2x}}(\sqrt{(e^x)^2})}=\frac{(e^{x})^2}{e^x\sqrt{1-e^{2x}}}=\frac{e^x}{\sqrt{1-e^{2x}}}$