Transcription of Derivatives Cheat Sheet - University of Connecticut
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Derivatives Cheat Sheet - University of Connecticut
Derivatives Cheat SheetDerivative Rules1. Constant Rule:ddx(c) = 0,wherecis a constant2. Power Rule:ddx(xn) =nxn 13. Product Rule:(fg) =f g+fg 4. Quotient Rule:(fg) =f g fg g25. Chain Rule:(f(g(x)) =f (g(x))g (x)Common DerivativesTrigonometric Functionsddx(sinx) = cosxddx(cosx) = sinxddx(tanx) = sec2xddx(secx) = secxtanxddx(cscx) = cscxcotxddx(cotx) = csc2xInverse Trigonometric Functionsddx(sin 1x) =1 1 x2ddx(cos 1x) = 1 1 x2ddx(tan 1x) =11 +x2 exponential & logarithmic Functionsddx(ax) =axln(a)ddx(ex) =exddx(loga(x)) =1xln(a)ddx(ln(x)) =1x1 Chain RuleIn the below,u=f(x)is a function ofx. These rules are all generalizations of the above rules using thechain (un) =nun (au) =auln(a) (eu) = (loga(u)) =1xln(u) (ln(u)) = (sin(u)) = cos(u) (cos(u)) = sin(u) (tan(u)) = sec2(u) idea for all other trig (tan 1(u)) =11 + idea for all other inverse trig functionsImplicit DifferentiationUse whenev)
Exponential & Logarithmic Functions d dx (a x) = a ln(a) d dx (ex) = ex d dx (log a (x)) = 1 xln(a) d dx (ln(x)) = 1 x 1. Chain Rule In the below, u = f(x) is a function of x. These rules are all generalizations of the above rules using the ... these derivatives. Log Differentiation Steps: 1. Take the ln of both sides 2. Simplify the problem ...
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