"Try differentiating y = x3. We let y grow to y + dy while x grows to x + dx. Then we have y + dy = (x + dx)3. ...[By a similar argument as above] dy/dx = 3x^2. ...Try differentiating y = x4. Starting as before by letting both y and x grow a bit, we have: y + dy = (x + dx)4. ...[By a similar argument as above] dy/dx = 4x^3."