Take a derivative

f[x_] = x ^ 3 - Sin[x ^ 2]

x^3 - Sin[x^2]

f'[x]

3*x^2 - 2*x*Cos[x^2]

f'''[x]

6 + 8*x^3*Cos[x^2] + 12*x*Sin[x^2]

D[f[x], x]

3*x^2 - 2*x*Cos[x^2]

D[f[x], {x, 3}]

6 + 8*x^3*Cos[x^2] + 12*x*Sin[x^2]

g[x_, y_] = (x + y) ^ 4

(x + y)^4

D[g[x, y], x, {y, 2}]

24*(x + y)

{HeavisideTheta[-1], HeavisideTheta[0], HeavisideTheta[1]}

{0, HeavisideTheta[0], 1}

HeavisideTheta'[x]

DiracDelta[x]

Plot[{HeavisideTheta[x], DiracDelta[x]}, {x, -2, 2}, PlotStyle -> {{Thickness[.02], Green}, {Thickness[.01], Red}}]

-Graphics-