Techniques of Differentiation 1.Definition of Derivative 2.Power Rule 3.Chain Rule 4.Product Rule 5.Quotient Rule

Techniques of Differentiation Definition of Derivative – lim f(x+h) – f(x) h  0h

Techniques of Differentiation Power Rule: – Original function f(x) = ax b – Derivative of function f’(x) = b*ax b-1

Techniques of Differentiation Chain Rule: – PTI – Stands for Power/Trig/InsideOfParentheses – Example: f(x) = (sin (4x)) 3 – Derivative is: 3(sin(4x)) 2 (cos(4x))(4) Power Rule Trig Derivative Angle Inside Derivative PTA

Techniques of Differentiation Product Rule: – Original Function has two terms being multiplied. – f(x) = a*b – Product Rule f’(x) = a*b’ + b*a’ – Example: f(x) = 3xsinx a b f’(x) = 3x*cosx + sinx*3 or 3xcosx + 3sinx a b’ a’ b

Techniques of Differentiation Quotient Rule – Original function f(x) has at least one variable in denominator. – f(x) = a b – Quotient Rule f’(x) = ba’ – ab’ b 2