Series[f[x],{x,0,5}]

ser=Series[Sin[x],{x,0,5}]
Normal[ser]

Integrate[Tanh[2.36*(2.456-i)],i]

Integrate[Tanh[a*(b-i)],i]

rules=Cases[Tanh[2.36*(2.456-i)],Tanh[aa_*(bb_-i)]:>{a->aa,b->bb},{0,∞}][[1]]

Integrate[Tanh[a*(b-i)],i]/.rules

DSolve[{Tanh[2.36*(2.456-t)]==y'[t],y[t1]==0},y[t],t]

eqn=y'[t]==((-1.)/10)Sin[10y[t]+Sin[10t]];
initCond=y[0.]==1;
(*DSolve[{eqn,initCond},y[t],t]*)
tmax=10;
sol=NDSolve[{eqn,initCond},y,{t,0,tmax}][[1]];
Plot[y[t]/.sol,{t,0,tmax}];

D[f[y[t],t],t]

derivativeFirst[{t_,y_}]=eqn[[2]]/.y[t]->y;

derivativeSecond[{t_,y_}]=(D[eqn[[2]],t]/.y'[t]->eqn[[2]])/.y[t]->y;

derivativeThird[{t_,y_}]=(D[derivativeSecond[{t,y[t]}],t]/.y'[t]->eqn[[2]])/.y[t]->y;

nSteps=50;
Δt=(tmax/nSteps);
step[point:{t_,y_}]:={t+Δt,y+Δt*derivativeFirst[point]};

startPoint=initCond/.{y[tStart_]==yStart_:>{tStart,yStart}};
sol=NestList[step,startPoint,nSteps];

initCond