University:
Eastern Kentucky University
Course:
MAT 234 | Calculus I
Academic year:

2020
Views:

316

Pages:

1
Author:

nomphethofou

List of DerivativeRules Below isalistofallthederivativerules wewent overin class. • Constant Rule: f (x)=c thenf ′ (x)=0 • Constant Multiple Rule: g(x)=c · f (x)theng ′ (x)=c · f ′ (x) • Power Rule: f (x)=xn thenf ′ (x)=nxn−1 • Sum and Difference Rule: h(x)=f (x)±g(x) thenh′ (x)=f ′ (x)±g ′ (x) • Product Rule: h(x)=f (x)g(x)thenh′ (x) =f ′ (x)g(x)+f (x)g ′ (x) • Quotient Rule: h(x)= f (x) g(x) thenh′ (x)= f ′ (x)g(x) − f (x)g ′ (x) g(x)2 • Chain Rule: h(x)=f (g (x))thenh′ (x)=f ′ (g (x))g ′ (x) • Trig Derivatives: – – – – – f (x)=sin(x)thenf ′ (x)=cos(x) f (x)=cos(x)thenf ′ (x)=− sin(x) f (x)=tan(x)thenf ′ (x)=sec2 (x) f (x)=sec(x)thenf ′ (x) =sec(x)tan(x) f (x)=cot(x)then f ′ (x)=− csc2 (x) – f (x)=csc(x)thenf ′ (x) =− csc(x)cot(x) • Exponential Derivatives – – – – f (x)=ax then f ′ (x)=ln(a)ax f (x)=ex then f ′ (x)=ex f (x)=ag(x) then f ′ (x)=ln(a)ag(x) g ′ (x) f (x)=eg(x) then f ′ (x)=eg(x) g ′ (x) • Logarithm Derivatives 1 – f (x)=loga (x)then f ′ (x)= – f (x)=ln(x)thenf ′ (x)= ln(a)x 1 – f (x)=loga (g(x))then f ′ (x)= – f (x)=ln(g(x))then f ′ (x)= x g ′ (x) ln(a)g (x) g ′ (x) g(x) 1

List of Derivative Rules

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