Derivatives Cheat Sheet, Study notes of Calculus

Download Derivatives Cheat Sheet and more Study notes Calculus in PDF only on Docsity! Derivatives Cheat Sheet Derivative Rules 1. Constant Rule: d dx (c) = 0, where c is a constant 2. Power Rule: d dx (xn) = nxn−1 3. Product Rule: (fg)′ = f ′g + fg′ 4. Quotient Rule: ( f g )′ = f ′g − fg′ g2 5. Chain Rule: (f(g(x))′ = f ′(g(x))g′(x) Exponential & Logarithmic Functions d dx (ax) = ax ln(a) d dx (ex) = ex d dx (loga(x)) = 1 x ln(a) d dx (ln(x)) = 1 x Chain Rule These rules are all generalizations of the above rules using the chain rule. 1. d dx ([g(x)]n) = n[g(x)]n−1g′(x) 2. d dx (ag(x)) = ag(x)g′(x) ln(a) 3. d dx (eg(x)) = eg(x)g′(x) 4. d dx (loga |g(x)|) = 1 g(x) ln(a) g′(x) 5. d dx (ln |g(x)|) = 1 g(x) g′(x) 1