Calculus:More Differentation Rules

1. REDIRECT Calculus/More Differentiation Rules

The product rule

The product of two differentiable funcations f and g is itself differentiable. Moreover, the derivative of fg is the first function times the derivative of the 2nd plus the 2nd fuction times the derivative of the 1st

y' of y = u x v u & v representing different fuctions like --> (x-3)(x+7)

y' = uv' + u'v

Example 1: Find y' of $y=(2x-7)(7x^2+8)$

    remember: y' = uv' + u'v

              $y^{\prime }=(2x-7)[(7*2)x]+(2)(7x^2+8)$ product rule
              $=(2x-7)(14x)+2(7x^2+8)$ simplify
              $=42x^2-98x+16$

The quotient rule

Similar to product rule,

y' of y = u / v u & v representing different fuctions like --> (x-3)(x+7)

y' = (u'v - uv') / v^2

Example 1: Find y' of $y=(3x)(2x^2)$

              $y^{\prime }=[(3)(2x^2)-(3x)(4x)]/(2x^2{)}^2$ quotient rule
              $=(6x^2-12x^2)/(4x^4)$ simplify
              <math>   = (-6x^2) / (4x^4)
                       = (-3)/(2x^2)