Chain, Product, Qoutient

Chain rule
1. Use when a function of x
  1. eg. y= (x^3 + 4)^7
  2. y= du/dx x dy/dx
2. Method:
  1. 1. Find u ( inner most function) 2. Rewrite y in terms of u
    1. 3. Differentiate y with respect to u dy/du 4. Differentiate u with respect to x du/dx
      1. 5. Multiply the two together dy/dx 6. Replace u with the correct term
Product rule
1. Use when functions of x are multiplied together
  1. eg. y= e^x x^8
  2. y= u(dv/dx) + v(du/dx)
  3. Method:
    1. 1. Find u and v ( two different functions) 2. Differentiate u with respect to x du/dx
      1. 3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = udv+vdu
Qoutient rule
1. Use when functions of x are being divided
  1. eg. y= x^3 +1 / 2x^2 +3
  2. y= vdv- udv / v^2
  3. Method:
    1. 1. Find u and v u=top function v=denominator 2.differntiate u with respect to x du/dx
      1. 3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = vdu-udv/ v^2
How to differentiate :
1. Take the power to the front then decrease the power by one

Resource summary

	Created by sammy414 almost 11 years ago