Question 383605
Find the derivatives of {{{y=sin(x)}}} where the number after {{{f}}} is the number of times {{{f}}} has been differentiated. 
{{{f1(x)=cos(x)}}}
{{{f2(x)=-sin(x)}}}
{{{f3(x)=-cos(x)}}}
{{{f4(x)=sin(x)}}}
{{{f5(x)=cos(x)}}}
Expanded about {{{x=0}}},
{{{f(x)=f(0)+f1(0)*x+f2(0)*(x^2/2!)+f3(0)*(x^3/3!)+f4(0)*(x^4/4!)+f5(0)*(x^5/5!)}}}
{{{f(0)=sin(0)=0}}}
{{{f1(0)=cos(0)=1}}}
{{{f2(0)=-sin(0)=0}}}
{{{f3(0)=-cos(0)=-1}}}
{{{f4(0)=sin(0)=0}}}
{{{f5(0)=cos(0)=1}}}
.
.
{{{f(x)=0+1*x+0*(x^2/2!)-1*(x^3/3!)+0*(x^4/4!)+1*(x^5/5!)}}}
{{{sin(x)=x-(x^3/3!)+(x^5/5!)}}}