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 + x^{3}) = d/dx (5x) + d/dx (x^{3}) = 5 d/dx (x) + 3x^{2}

= 5(1) + 3x^{2 }= 5 + 3x^{2}