Demo of differentiation and basic plotting with Mathematica

Differentiation with Mathematica

Clear[f]
f[x_] =  x^5 - 5 x^4 +  5 x + 3

D[f[x], x]

D[Sin[x] x^2, x]

D[((Sin[x])/(1+ x^2)), x]
%//Together

Some basic plotting

Clear[f]
f[x_] =  x^5 - 5 x^4 +  5 x + 3

g[x_] = D[f[x], x]

Plot[{f[x], g[x]},  {x, -2, 6}]

Plot[{f[x], g[x]},  {x, -1.5, 1.5}]