Question

If u, v and w are functions of x, then show that

d/dx (u.v.w) = du/dx v.w+u. dv/dx .w+u.v.dw/dx

in two ways-first by repeated application of product rule, second by logarithmic differentiation.

Answer 1

Let y = u.v.w =u.(v.w)

By applying product rule, we obtain

Differentiating both sides with respect to x, we obtain