∂^9f/∂x^9(x^sin(x))=
(x^sin(x)*sin(x)^9+((9*x^(sin(x)+1)*cos(x)-36*x^(sin(x)+2))*log(x)-36*x^sin(x))*sin(x)^8+((36*x^(sin(x)+2)*cos(x)^2-252*x^(sin(x)+3)*cos(x)+378*x^(sin(x)+4))*log(x)^2+(756*x^(sin(x)+2)-252*x^(sin(x)+1)*cos(x))*log(x)+72*x^(sin(x)+1)*cos(x)+x^sin(x)*(546-252*x^2))*sin(x)^7+((84*x^(sin(x)+3)*cos(x)^3-756*x^(sin(x)+4)*cos(x)^2+1890*x^(sin(x)+5)*cos(x)-1260*x^(sin(x)+6))*log(x)^3+((-756*x^(sin(x)+2)*cos(x)^2)+3780*x^(sin(x)+3)*cos(x)-3780*x^(sin(x)+4))*log(x)^2+(504*x^(sin(x)+2)*cos(x)^2+x^sin(x)*(2898*x-3108*x^3)*cos(x)+x^sin(x)*(3906*x^4-6300*x^2))*log(x)-1764*x^(sin(x)+1)*cos(x)+x^sin(x)*(4536*x^2-4536))*sin(x)^6+((126*x^(sin(x)+4)*cos(x)^4-1260*x^(sin(x)+5)*cos(x)^3+3780*x^(sin(x)+6)*cos(x)^2-3780*x^(sin(x)+7)*cos(x)+945*x^(sin(x)+8))*log(x)^4+((-1260*x^(sin(x)+3)*cos(x)^3)+7560*x^(sin(x)+4)*cos(x)^2-11340*x^(sin(x)+5)*cos(x)+3780*x^(sin(x)+6))*log(x)^3+(1512*x^(sin(x)+3)*cos(x)^3+x^sin(x)*(6300*x^2-11844*x^4)*cos(x)^2+x^sin(x)*(24570*x^5-21420*x^3)*cos(x)+x^sin(x)*(13230*x^4-12600*x^6))*log(x)^2+((-9072*x^(sin(x)+2)*cos(x)^2)+x^sin(x)*(39060*x^3-17640*x)*cos(x)+x^sin(x)*(26460*x^2-31500*x^4))*log(x)+1512*x^(sin(x)+2)*cos(x)^2+x^sin(x)*(17388*x-8064*x^3)*cos(x)+x^sin(x)*(8190*x^4-31500*x^2+22449))*sin(x)^5+((126*x^(sin(x)+5)*cos(x)^5-1260*x^(sin(x)+6)*cos(x)^4+3780*x^(sin(x)+7)*cos(x)^3-3780*x^(sin(x)+8)*cos(x)^2+945*x^(sin(x)+9)*cos(x))*log(x)^5+((-1260*x^(sin(x)+4)*cos(x)^4)+7560*x^(sin(x)+5)*cos(x)^3-11340*x^(sin(x)+6)*cos(x)^2+3780*x^(sin(x)+7)*cos(x))*log(x)^4+(2520*x^(sin(x)+4)*cos(x)^4+x^sin(x)*(7140*x^3-21420*x^5)*cos(x)^3+x^sin(x)*(51660*x^6-26460*x^4)*cos(x)^2+x^sin(x)*(20790*x^5-37800*x^7)*cos(x)+x^sin(x)*(5670*x^8-2520*x^6))*log(x)^3+((-18900*x^(sin(x)+3)*cos(x)^3)+x^sin(x)*(95760*x^4-26460*x^2)*cos(x)^2+x^sin(x)*(56700*x^3-113400*x^5)*cos(x)+x^sin(x)*(26460*x^6-18900*x^4))*log(x)^2+(7560*x^(sin(x)+3)*cos(x)^3+x^sin(x)*(63000*x^2-50400*x^4)*cos(x)^2+x^sin(x)*(83286*x^5-178500*x^3+60921*x)*cos(x)+x^sin(x)*((-30324*x^6)+83790*x^4-58464*x^2))*log(x)-22680*x^(sin(x)+2)*cos(x)^2+x^sin(x)*(81900*x^3-88200*x)*cos(x)+x^sin(x)*((-50400*x^4)+105840*x^2-67284))*sin(x)^4+((84*x^(sin(x)+6)*cos(x)^6-756*x^(sin(x)+7)*cos(x)^5+1890*x^(sin(x)+8)*cos(x)^4-1260*x^(sin(x)+9)*cos(x)^3)*log(x)^6+((-756*x^(sin(x)+5)*cos(x)^5)+3780*x^(sin(x)+6)*cos(x)^4-3780*x^(sin(x)+7)*cos(x)^3)*log(x)^5+(2520*x^(sin(x)+5)*cos(x)^5+x^sin(x)*(4410*x^4-20580*x^6)*cos(x)^4+x^sin(x)*(46620*x^7-13860*x^5)*cos(x)^3+x^sin(x)*(7560*x^6-30240*x^8)*cos(x)^2+3150*x^(sin(x)+9)*cos(x))*log(x)^4+((-20160*x^(sin(x)+4)*cos(x)^4)+x^sin(x)*(98280*x^5-18900*x^3)*cos(x)^3+x^sin(x)*(37800*x^4-109620*x^6)*cos(x)^2+x^sin(x)*(22680*x^7-11340*x^5)*cos(x))*log(x)^3+(15120*x^(sin(x)+4)*cos(x)^4+x^sin(x)*(85680*x^3-105840*x^5)*cos(x)^3+x^sin(x)*(194124*x^6-255780*x^4+58464*x^2)*cos(x)^2+x^sin(x)*((-92988*x^7)+145530*x^5-69048*x^3)*cos(x)+x^sin(x)*(6237*x^8-10080*x^6+9072*x^4))*log(x)^2+((-75600*x^(sin(x)+3)*cos(x)^3)+x^sin(x)*(312480*x^4-211680*x^2)*cos(x)^2+x^sin(x)*((-272916*x^5)+359100*x^3-118188*x)*cos(x)+x^sin(x)*(38052*x^6-81900*x^4+63504*x^2))*log(x)+10080*x^(sin(x)+3)*cos(x)^3+x^sin(x)*(126000*x^2-55440*x^4)*cos(x)^2+x^sin(x)*(68544*x^5-285600*x^3+243684*x)*cos(x)+x^sin(x)*((-15372*x^6)+92610*x^4-175392*x^2+118124))*sin(x)^3+((36*x^(sin(x)+7)*cos(x)^7-252*x^(sin(x)+8)*cos(x)^6+378*x^(sin(x)+9)*cos(x)^5)*log(x)^7+(756*x^(sin(x)+7)*cos(x)^5-252*x^(sin(x)+6)*cos(x)^6)*log(x)^6+(1512*x^(sin(x)+6)*cos(x)^6+x^sin(x)*(1386*x^5-10332*x^7)*cos(x)^5+x^sin(x)*(17010*x^8-2520*x^6)*cos(x)^4-5040*x^(sin(x)+9)*cos(x)^3)*log(x)^5+((-11340*x^(sin(x)+5)*cos(x)^5)+x^sin(x)*(42840*x^6-6300*x^4)*cos(x)^4+x^sin(x)*(7560*x^5-27720*x^7)*cos(x)^3)*log(x)^4+(15120*x^(sin(x)+5)*cos(x)^5+x^sin(x)*(52920*x^4-95760*x^6)*cos(x)^4+x^sin(x)*(149436*x^7-124740*x^5+23016*x^3)*cos(x)^3+x^sin(x)*((-52164*x^8)+42840*x^6-18144*x^4)*cos(x)^2+2205*x^(sin(x)+9)*cos(x))*log(x)^3+((-90720*x^(sin(x)+4)*cos(x)^4)+x^sin(x)*(340200*x^5-170100*x^3)*cos(x)^3+x^sin(x)*((-253512*x^6)+252000*x^4-63504*x^2)*cos(x)^2+x^sin(x)*(24948*x^7-45360*x^5+30240*x^3)*cos(x))*log(x)^2+(30240*x^(sin(x)+4)*cos(x)^4+x^sin(x)*(257040*x^3-166320*x^5)*cos(x)^3+x^sin(x)*(212184*x^6-582120*x^4+350784*x^2)*cos(x)^2+x^sin(x)*((-54468*x^7)+209286*x^5-299208*x^3+117612*x)*cos(x)+x^sin(x)*(1143*x^8-5208*x^6+21168*x^4-25920*x^2))*log(x)-75600*x^(sin(x)+3)*cos(x)^3+x^sin(x)*(241920*x^4-317520*x^2)*cos(x)^2+x^sin(x)*((-138348*x^5)+396900*x^3-354564*x)*cos(x)+x^sin(x)*(8064*x^6-50400*x^4+127008*x^2-109584))*sin(x)^2