Differentiation

Differentiation

1. basic diff formulas

   • chain Rule
     • g[f(x)} = g'[f(x)]*f'(x)
   • Product Rule
     • f(x)*g(x) = f'(x)*g(x) + f(x)*g'(x)
       • UV = U'V + UV'
   • Quotient Rule
     • f(x)/g(x) = {f'(x)*g(x) - f(x)*g'(x)}/[g(x)]^2
       • U/V = {U'V - UV'}/V^2

2. Notation

   • f'(x)
   • dy/dx
   • d/dx
   • y'
   • Dx{f(x)}

3. diff Rules

   • Exponential and Logarithmic Functions
   • trig functions
   • second Derivitives
     • f''(x)
     • [d^2y] / [dx^2]
     • To double diff simply diff your original function and then diff it again to finf the double diff.
   • Basic functions
   • on graphs
     • f'(x) = 0 stationary point
       • nature of stationary points
         • maximum when double diff < 0
         • minimum when double diff > 0
   • applications
     • diff = 0 to find speed and velocity
     • double diff to get the acceleration
     • continuous - differentiable
     • dis-continuous- non differentiable
     • average rate of change = (y2-y1)/(x2-x1)
   • tangents to curves
     • gradient of tangent = diff at certain point.
       • equation y=mx+c using gradient found above sub in points to find C
         • equation of normal flip the gradient of tangent and use same method to find equation.