Math 19a Calculus

Math 19a Calculus

1. Derivatives

   • A function that represents the rate of change of the parent function, can use d/dx, dy/dx, or f'(x) notation most commonly
   • Chain Rule
     • A differential rule in which f(x)=g(h(x)), f'(x)=g'(h(x))[h'(x)]
       • Used very frequently in implicit derivatives, and derivatives overall as each rule often works with others
   • Power Rule
     • A differential rule in which f(x)=x^n, f'(x)=nx^(n-1)
       • Used most frequently in polynomials
   • Product Rule
     • A differential rule in which d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)
   • Quotient Rule
     • A differential rule in which d/dx[f(x)/g(x)]=[f'(x)g(x)+f(x)g'(x)]/(g(x))^2
   • Rates Of Change
     • Using a tangent line, an unknown value of f(x) can be approximated through f(a+h)~f(a)+f'(a)h
   • Inverse Derivatives
     • A differential rule in which [f^(-1)]'(x)=1/[f'(f^(-1)(x))]
   • Implicit Derivatives
     • The derivative of a non-function, or equation with y and x on both sides that implies all sub functions with restricted domains and their derivatives