Answer to Question #60812 in Calculus for Raigeda Venckute

Question

The Taylor series about 0 for the function f(x)=sin(x) is x^2-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880.... and the Taylor series about 0 for the function g(x)=e^x is 1+x+(x^2)/2+(x^3)/6+(x^4)/24+(x^5)/120+....What is the coefficient of x^3 in the series for e^x sin(x)?