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Level 412

Logarithmic, Exponential & Inverse Trigonometric F


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They are inverses of each other.
What is the relationship between ln x (natural log) and e^x?
e^x
ƒ'(x) of e^x
e^u (du/dx)
ƒ'(x) of e^u
∫e^x dx
e^x + C
∫e^u du
e^u + C
1/(ln a)x
ƒ'(x) of log(base a) x
(ln a)(a^x)
ƒ'(x) of a^x
(ln a)(a^u)(du/dx)
ƒ'(x) of a^u
1/(ln a)u (du/dx)
ƒ'(x) of log(base a) x
nxⁿ⁻¹
ƒ'(x) of xⁿ
nuⁿ⁻¹ (du/dx)
ƒ'(x) of uⁿ
A=P(1+(r/n))^(nt)
Interest compounded n times per year
A=Pe^rt
What is the application (formula) to use when the interest is compounded continuosly?
u'/√a²-u²
ƒ'(x) of arcsinx
-u'/√a²-u²
ƒ'(x) of arccosx
u'/a²+u²
ƒ'(x) of arctanx
-u'/(|u|√u²-a²)
ƒ'(x) of arccscx
u'/(|u|√u²-a²)
ƒ'(x) of arcsecx
-u'/√a²+u²
ƒ'(x) of arccotx
∫u'/√a²-u²
arcsin (u/a) + C
∫-u'/√a²-u²
none
∫u'/a²+u²
(1/a) arctan (u/a) + C
∫-u'/(|u|√u²-a²)
none
∫u'/(|u|√u²-a²)
(1/a) arcsec (|u|/a) + C
∫-u'/√a²+u²
none
cos x
f'(x) of sin x
- sin x
f'(x) of cos x
sec² x
f'(x) of tan x
cscxcotx
f'(x) of csc x
secxtanx
f'(x) of sec x
-csc²x
f'(x) of cot x
∫sin x dx
-cos x + C
∫ cos x dx
sin x + C
∫ tan x dx
-ln |cos u| + C
∫sec x dx
ln |sec x + tan x| + C
∫csc x dx
-ln |csc x + cot x| + C
∫cot x dx
ln |sin x| + C