AP Calculus BC Study Guide with complete solutions

AP Calculus BC Study Guide with complete solutions

sin² θ + cos² θ = - Answer-1

/.1 + tan² θ = - Answer-sec² θ

/.1 + cot² θ = - Answer-csc² θ

/.sin(-θ) = - Answer--sin θ

/.cos(-θ) = - Answer-cos θ

/.tan(-θ) = - Answer--tan θ

/.sin(A + B) = - Answer-sinAcosB + sinBcosA

/.sin(A - B) = - Answer-sinAcosB - sinBcosA

/.cos(A + B) = - Answer-cosAcosB - sinAsinB

/.cos(A - B) = - Answer-cosAcosB + sinAsinB

/.sin 2θ = - Answer-2sinθcosθ

/.cos 2θ = - Answer-cos² θ - sin² θ
= 2cos² θ - 1
= 1 - 2sin² θ

/.tan θ = - Answer-sin θ / cos θ
= 1 / cot θ

/.cot θ = - Answer-cos θ / sin θ
= 1 / tan θ

/.sec θ = - Answer-1 / cos θ

/.csc θ = - Answer-1 / sin θ

/.cos² θ = - Answer-()(1 + cos 2θ)

/.sin² θ = - Answer-()(1 - cos 2θ)

/.d/dx (x^n) = - Answer-nx^(n - 1)

, /.d/dx (fg) = - Answer-fg' + gf'

/.d/dx (f / g) = - Answer-(gf' - fg') / g^2

/.d/dx f(g(x)) = - Answer-f'(g(x))g'(x)

/.d/dx (sin x) = - Answer-cos x

/.d/dx (cos x) = - Answer--sin x

/.d/dx (tan x) = - Answer-sec² x

/.d/dx (cot x) = - Answer--csc² x

/.d/dx (sec x) = - Answer-secxtanx

/.d/dx (csc x) = - Answer--cscxcotx

/.d/dx (e^x) = - Answer-e^x

/.d/dx (a^x) = - Answer-a^x * ln a

/.d/dx (ln x) = - Answer-1 / x

/.d/dx (Arcsin x) = - Answer-1 / √(1 - x²)

/.d/dx (Arctan x) = - Answer-1 / (1 + x²)

/.d/dx (Arcsec x) = - Answer-1 / (|x| * √(x² - 1))

/.d/dx (Arccos x) = - Answer--1 / √(1 - x²)

/.d/dx (Arccot x) = - Answer-1 / (1 + x²)

/.d/dx (Arccsc x) = - Answer--1 / (|x| * √(x² - 1))

/.d/dx [c] = - Answer-0

/.d/dx [cf(x)] = - Answer-cf'(x)

/.∫a dx = - Answer-ax + C

/.∫x^n dx = - Answer-(x^n+1) / (n + 1) + C,
n≠1

/.∫1 / x dx = - Answer-ln |x| + C