Differentiation of a Quadratic: v_0 = V_DD - (1/V_x)[(v_1 - V_t)v_0 - (1/2)(v_0)^2]

[studentofece]

I'm working on a digital electronics question and I'm confused by how differentiation lead to one of the terms in the solution.

It seems that they replaced vi with VIH and dvo/dvi with -1 but I'm not sure where vo (the second term in the brackets of the second equation) comes from

 

[Dr.Peterson]

I'm working on a digital electronics question and I'm confused by how differentiation lead to one of the terms in the solution.
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It seems that they replaced vi with VIH and dvo/dvi with -1 but I'm not sure where vo (the second term in the brackets of the second equation) comes from

They applied the product rule to [imath](v_1-V_1)v_o[/imath], since both factors are functions of [imath]v_1[/imath]:


becomes

 

[studentofece]

I incorrectly assumed it came from the 1/2vo^2 term and that was the source of my confusion. Thank you for clarifying Dr. Peterson.

 

[Dr.Peterson]

I incorrectly assumed it came from the 1/2vo^2 term and that was the source of my confusion. Thank you for clarifying Dr. Peterson.

I initially misread it too, and had to delete everything I'd written when I realized it wasn't what you were asking about.

For that matter, it was only much later that I realized what I'd read as 0 and 1 are really O and I, or t, or maybe l. I'll blame the fact that I'm in the middle of cataract surgeries, so nothing is quite in focus.

But really, no one should ever use 0, o, O, 1, I, l, or t as subscripts, or maybe anywhere else either.