The derivative of the sum of two differentiable functions is the sum of their derivative, i.e. if u and v be two differentiable functions of x, then
d/dx ( u ± v) = du/dx ± dv/dx
Note. The above formulae can be extended to a sum of three, or more differentiable function. Hence, the derivative of a sum of several differentiable functions is the algebraic sum of the derivatives of the individual functions.
i.e. if, y = u ± v ± w ± Z ± …. Then
dy/dx = du/dx ± dv/dx ± dw/dx ± dz/dx ± …..
(i) When y = 5x + x³,
dy/dx = d/ dx (5x + x3) = d/dx (5x) + d/dx (x3) = 5 d/dx (x) + 3x2
= 5(1) + 3x2 = 5 + 3x2