If u, v, and w are function of x, then show that d/dx(u,v,w) = du/dx(v.w) + u,(dy/dx)w + u.v(dw/dx)

Question

If u, v, and w are function of x, then show that
\(\frac{d}{dx}(u, v, w)\) = \(\frac{d}{dx}v.w + u.\frac{dv}{dx}w + u.v\frac{dw}{dx}.\) in two ways – first by repeated application of product rule, second by logarithmic differentiation.

Answer 1

Let y = uvw (Logarithmic differentiation) log 

log y = log u +log v + low w