Section 3.3: Derivatives of Products and Quotients

Product Rule

If y = f(x) = F(x)S(x) and if F'(x) and S'(x) exist, then

f'(x) = F(x)S'(x) + S(x)F'(x)

Using simplified notation,

y' = FS' + SF'or dy/dx = F dS/dx + S dF/dx

Quotient Rule

If y = f(x) = T(x)/B(x) and if T'(x) and B'(x) exist, then

f'(x) = [B(x)T'(x) - T(x)B'(x)]/[B(x)]²

Using simplified notation,

y' = [BT' - TB']/B²or dy/dx = [B dT/dx - T dB/dx]/B²