Partial differentiation problem (FOC)

Question

I am having troubles to partially differentiate the following:

$ \frac{\delta (v_i-4b_i)^{1/2}*\frac{b_i-c}{a}}{\delta b_i}=0 $

Mostly I am unsure, which rules are applied here and in what order. So far, I made some attempts, but without any success. Maybe someone can help me understanding the applied procedure here and show me how to do it and what the result is.

You want the partial of the whole numerator? – Vishu Jan 26 '21 at 11:41 — Vishu, Jan 26 '21 at 11:41
Yes, the whole numerator differentiated with respect to b_i – Phil Jan 26 '21 at 12:40 — Phil, Jan 26 '21 at 12:40

score 1 · Accepted Answer · answered Jan 26 '21 at 12:58

1

$$\frac{\partial }{\partial b_i}\left( \sqrt{v_i -4b_i}\cdot \frac{b_i-c}{a}\right) \\ = \frac{\partial (\sqrt{v_i-4b_i})}{\partial b_i}\cdot \frac{b_i-c}{a} + \frac{\partial (\frac{b_i-c}{a} ) }{\partial b_i} \cdot \sqrt{v_i-4b_i} \\ = \frac{-4}{2\sqrt{v_i-4b_i}} \cdot \frac{b_i-c}{a} + \frac 1a \cdot\sqrt{v_i-4b_i}$$

answered Jan 26 '21 at 12:58

Vishu

14,469

1

Thanks a lot, now I see my mistake! – Phil Jan 26 '21 at 13:12

Partial differentiation problem (FOC)

1 Answers1