ClearAll[f];
f[t_]:=Sin[(t^2)];
Plot[f[(y^(1/3))],{y,0,4Pi},AxesLabel->{"y","f[(y^(1/3))]"},PlotStyle->Thick];
der=D[f[(y^(1/3))],y];
Plot[{der,f[(y^(1/3))]},{y,0,4Pi},AxesLabel->{"y","f[(y^(1/3))]"},PlotStyle->Thick];
Plot[f'[(y^(1/3))],{y,0,4Pi},AxesLabel->{"y","f[(y^(1/3))]"},PlotStyle->{Thick,Red}]

D[f[(y^(1/3))],y]
f'[(y^(1/3))]

Select[{1,2,4,7,6,2},#>2&]

test[x_]:=x>2;
Select[{1,2,4,7,6,2},test]

((#)^2)&[5]

Plot3D[((#1)^2)+#2&[x,y],{x,-1,1},{y,-1,1}]

Sin@5
Sin[5]
5//Sin

N[Pi,10]

{x,0,2Pi}//Plot[Sin[x],#]&

Pi//N[#,10]&

ClearAll[f]
f[x_,y_]:=y+(x^2);
Plot3D[f[x,y],{x,-1,1},{y,-1,1}]
Plot3D[((#1)^2)+#2&[x,y],{x,-1,1},{y,-1,1}]

Sin'

ClearAll[f]
f[{a_,b_}]:={b,a}
f[{1,2}]

NestList[Cos,0.,15]

ClearAll[der,step]
der[{t_,y_}]:=-5y;
step[{t_,y_}]:={t+Δt,y+Δt*der[{t,y}]};
start={0,100};
tmax=1.;
n=200;
Δt=(tmax/n);
solution=NestList[step,start,n];
ListPlot[solution,PlotRange->All]