Determinare la derivata rispetto a x di:
  (a)  sin(2x − 1)       (b)  (3x² − 4x + 1)⁸       (c)  √(sin²(3x) + x)

(a)  D_x(sin(2x − 1)) = D_u(sin(u))·D_x(2x − 1) = cos(u)·2 = 2·cos(2x − 1)

(b)  D_x((3x² − 4x + 1)⁸) = D_u(u⁸)·D_x(3x² − 4x + 1) = 8(3x² − 4x + 1)⁷·(6x − 4)

(c)  D_x√(sin²(3x) + x) = D_u√(u) · (D_v(v²)·D_x(sin(3x)) + D_x(x)) = -1/(2√u) · (2·v·3·cos(3x) + 1) = (6·sin(3x)cos(3x) + 1) / (2√(sin²(3x) + x)

Puoi verificare i risultati con WolframAlpha, battendo, ad es.:
d/dx sqrt(sin(3*x)^2+x).