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Level 597

Calculus BC : Differentiation & Integration Formul


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d/dx (x^n)
= nx^(n-1)
d/dx (fg)
= fg' + gf'
d/dx (f/g)
= (gf' - fg')/ g^2
d/dx [f(g(x))]
= f'(g(x)) g'(x)
d/dx (sin(x))
= cos(x)
d/dx (cox(x))
= - sin(x)
d/dx (tan(x))
= sec^2 (x)
d/dx (cot(x))
= - csc^2(x)
d/dx (sec(x))
= sec(x) tan(x)
d/dx (csc(x))
= - csc(x) cot(x)
d/dx (e^x)
= e^x
d/dx (a^x)
= a^x lna
d/dx (ln(x))
= 1 / x
d/dx (Arcsin x)
= 1/ (square root of (1 - x^2))
d/dx (Arctan x)
= 1/ 1 + x^2
∫ a dx
= ax + C
∫ x^n dx
(x^n+1/ n+1) + c
∫ 1/x dx
ln lxl + c
∫ e^x dx
e^x + C
∫ a^x dx
(a^x/ lna) + c
∫ lnx dx
= xlnx - x + C
∫ sinx dx
= -cos x + C
∫ cosx dx
= sinx + C
∫ tanx dx
= ln (absolute value of secx) + C = - ln (absolute value of cosx) + C
∫ cotx dx
= ln (absolute value of sinx) + C
∫ secx dx
= ln (absolute value of sec x + tan x) + C
∫ cscx dx
= ln (absolute value of cscx - cotx) + C
∫ sec^2 (x) dx
= tanx + C
∫ secxtanx dx
= secx + C
∫ csc^2 (x) dx
= - cotx + C
∫ cscxcotx dx
= - cscx + C
∫ tan^2 (x) dx
= tanx - x + C
∫ dx / (a^2 + x^2)
= (1 / a) Arctan (x/a) + C
= Arcsin (x/a) + C
∫ dx / (the square root of ( a^2 - x^2) )
1
sin² x + cos² x
csc² x
1 + cot² x (pythagorean)
sec² x
tan² x + 1
tan x
sin x/cos x
cot x
cos x/sin x