#knowledgeacquired

x^2 + xy +xy^3 = 3

2x + dy/dx(x) + y + y^3 + 3xy^2(dy/dx) = 0

2x + y + y^3 = -dy/dx(x) - 3xy^2(dy/dx)

2x + y + y^3 = -dy/dx (x + 3xy^2)

dy/dx= ((-2x + y + y^3)/(x + 3xy^2))

Important Steps:

1) Differentiate each term

2) Every derivative of y needs a dy/dx

3) Isolate the terms with dy/dx by subtraction

4) Factor out the dy/dx

Important Steps:

1) Generate derivative for g(x)

2) Find g(x) for each derivative

3) Apply derivatives to Taylor Series (or Maclaurin Series) formula

Glycolysis - Cytoplasm - 2ATP - 2NADH

Acetyl CoA - Cytoplasm - 0ATP - 2NADH

Krebs Cycle - Mitochondrial Matrix - 2ATP - 6NADH + 2FADH2

Oxidative Phosphorylation - Mitochondrial membrane (cristae) - 32 ATP

Oxidative Phosphorylation: energy is not only stored in ATP, but also in electron/hydrogen carriers like NAD* and FAD. Electrons are transferred from electron carriers to oxygen, which results in the synthesis of ATP. 

The Electron Transport Chain: Throughout the process of cell respiration, many electrons have been carried in and out of the cycles. They have maintained their original energy in the form of readily available hydrogen carrier molecules. The two carriers are NADH and FADH2. (Notice how throughout the process each carrier gained a hydrogen, NAD* -> NADH and FAD -> FADH2). 

Important:

1) Two NADH molecules from glycolysis

2) Two NADH molecules from the production of acetyl CoA

3) Six NADH molecules from the Krebs Cycle

4) Two FADH2 molecules from the Krebs Cycle

5) Twelve Electron Carriers in total

Each molecule moves down the Electron Transport Chain which is a series of protein carriers in the cristae that break down the energy into a usable form. 

Chemiosmosis: allows ATP Synthase to occur, which is the final part of oxidative phosphorylation, the conversion of ADP to ATP. 

Important:

1) Every NADH yields 3ATP (except in glycolysis, only 2ATP)

2) Every FADH2 yields 2ATP