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22 Cards in this Set

  • Front
  • Back

d/dx xⁿ

nxⁿ⁻¹

Power Rule

d/dx eᵏˣ

keᵏˣ



k is a constant

d/dx eᵘ

eᵘ (du/dx)

Do not forget the chain rule

d/dx ln|u|

(1/u) (du/dx)
[u ≠ 0]

Do not forget the chain rule

d/dx sin(u)

cos(u) (du/dx)

Do not forget the chain rule

d/dx cos(u)

−sin(u) (du/dx)

Do not forget the chain rule

d/dx arcsin(u)

1/√[1 − u²] (du/dx)

Do not forget the chain rule

d/dx arccos(u)

−1/√[1 − u²] (du/dx)

Do not forget the chain rule

d/dx arctan(u)

1/(1 + u²) (du/dx)

Do not forget the chain rule

d/dx sec(u)

sec(u)tan(u) (du/dx)

Do not forget the chain rule

d/dx tan(u)

sec²(u) (du/dx)

Do not forget the chain rule

∫ xⁿ (dx)

(xⁿ⁺¹)/(n + 1) + C
[n ≠ −1]

∫ du/u

ln|u| + C
[u ≠ 0]

∫ cos(kx) (dx)

(1/k) sin(kx) + C

∫ tan(u) (du)

ln|sec(u)| + C

∫ aᵘ (du)

aᵘ/ln(a) + C

∫ eᵏˣ (dx)

(1/k) eᵏˣ + C

∫ sin(kx) (dx)

(−1/k) cos(kx) + C

∫ sec²(u) (du)

tan(u) + C

∫ sec(u) (du)

ln|sec(u) + tan(u)| + C

∫ 1/√[1 − u²] (du)

arcsin(u) + C

∫ −1/√[1 − u²] (du)

arccos(u) + C