A2 Maths Quick Question?

Question

When V = we^(w/10)

What is dV/dw?

(I am getting confused as to whether i should use the chain or product rule)

Answer 1

dV/dw= e^(w/10) +1/10 w* e^(w/10)

Answer 2

product rule and chain rule are the same thing in different guises...
let Z=ab; then (chain rule):
dZ/dx = d(Z)/da x da/dx + d(Z)/db x db/dx
i.e.
dZ/dx = bda/dx + adb/dx ... multiplication rule, as you call it

Your specific problem, from first principles:

V = we^(w/10)
V+dV = (w+dw)e^{(w+dw)/10) = (w+dw)e^(w/10)e^(dw/10)
approximate... e^x = 1+x for small x
V+dV = (w+dw)(e^(w/10)(1+dw/10))
V+dV = (w+dw)(e^(w/10) + dwe^(w/10)/10)
V+dV = we^(w/10) + wdwe^(w/10)/10 + dwe^(w/10) + (dw)^2e^(w/10)/10
ignore terms in (dw)^2 (they vanish as dw->0) and note that V = we^(w/10);
dV = dw[e^(w/10) + we^(w/10)/10]
i.e.
dV/dw = e^(w/10) + we^(w/10)/10

Applying the multiplication rule, with a = w and b = e^(w/10) is much tidier!