Math Problem Solver

Assuming the variable \(y\) refers to the function of the same name. If this is incorrect, please retry your query. Either include arguments for all function calls (i.e. \(f(x) \cdot g(x)\) instead of \(f \cdot g\)) or use different variables in the expression to be evaluated.

$$\begin{aligned}{y\left( x \right)}^{11}&=177147 x^{11} e^{22} + 649539 x^{10} e^{20} \sin{\left(x \right)} + 1082565 x^{9} e^{18} \sin^{2}{\left(x \right)} + 1082565 x^{8} e^{16} \sin^{3}{\left(x \right)} + 721710 x^{7} e^{14} \sin^{4}{\left(x \right)} + 336798 x^{6} e^{12} \sin^{5}{\left(x \right)} + 112266 x^{5} e^{10} \sin^{6}{\left(x \right)} + 26730 x^{4} e^{8} \sin^{7}{\left(x \right)} + 4455 x^{3} e^{6} \sin^{8}{\left(x \right)} + 495 x^{2} e^{4} \sin^{9}{\left(x \right)} + 33 x e^{2} \sin^{10}{\left(x \right)} + \sin^{11}{\left(x \right)}\end{aligned}$$

$$\begin{aligned}{y\left( x \right)}^{11}&=\left(\sin{\left(x \right)} + 3 e^{2} x\right)^{11}\\{y\left( x \right)}^{11}&=177147 x^{11} e^{22} + 649539 x^{10} e^{20} \sin{\left(x \right)} + 1082565 x^{9} e^{18} \sin^{2}{\left(x \right)} + 1082565 x^{8} e^{16} \sin^{3}{\left(x \right)} + 721710 x^{7} e^{14} \sin^{4}{\left(x \right)} + 336798 x^{6} e^{12} \sin^{5}{\left(x \right)} + 112266 x^{5} e^{10} \sin^{6}{\left(x \right)} + 26730 x^{4} e^{8} \sin^{7}{\left(x \right)} + 4455 x^{3} e^{6} \sin^{8}{\left(x \right)} + 495 x^{2} e^{4} \sin^{9}{\left(x \right)} + 33 x e^{2} \sin^{10}{\left(x \right)} + \sin^{11}{\left(x \right)}\\\end{aligned}$$

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).