Chain, Product, Qoutient

Chain, Product, Qoutient

1. Chain rule

   • Use when a function of x
     • eg. y= (x^3 + 4)^7
     • y= du/dx x dy/dx
   • Method:
     • 1. Find u ( inner most function) 2. Rewrite y in terms of u
       • 3. Differentiate y with respect to u dy/du 4. Differentiate u with respect to x du/dx
         • 5. Multiply the two together dy/dx 6. Replace u with the correct term

2. Product rule

   • Use when functions of x are multiplied together
     • eg. y= e^x x^8
     • y= u(dv/dx) + v(du/dx)
     • Method:
       • 1. Find u and v ( two different functions) 2. Differentiate u with respect to x du/dx
         • 3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = udv+vdu

3. Qoutient rule

   • Use when functions of x are being divided
     • eg. y= x^3 +1 / 2x^2 +3
     • y= vdv- udv / v^2
     • Method:
       • 1. Find u and v u=top function v=denominator 2.differntiate u with respect to x du/dx
         • 3. Differentiate v with respect to x dv/dx 4. Replace the terms in dy/dx = vdu-udv/ v^2

4. How to differentiate :

   • Take the power to the front then decrease the power by one