Найти производную: e^ctgx*sin4x

[latex](e^{ctgx}*sin4x)`=(e^{ctgx})`*sin4x+e^{ctgx}*(sin4x)`=\\=e^{ctgx}*(ctgx)`*sin4x+e^{ctgx}*cos4x*(4x)`=\\\\= -\frac{e^{ctgx}*sin4x}{sin^2x}+4e^{ctgx}*cos4x=e^{ctgx}(4cos4x- \frac{sin4x}{sin^2x}) [/latex]