Y=f(x) must be continuous at each:
-Critical Point or undefined and endpoints
Local Minimum
Goes (-,0,+) or (-, und, +)
Local Maximum
Goes (+,0,-) or (+, und, -)
Point of Inflection
Concavity Changes
(+,0,-) or (-,0,+)
(+,und,-) or (-,und,+)
D/dx(sinx)
Cosx
D/dx(cosx)
-sinx
D/dx(tanx)
SecĀ²x
D/dx(cotx)
-cscĀ²x
D/dx(secx)
Secxtanx
D/dx(cscx)
-cscxcotx
D/dx (lnx)
1/x Ć derivative of x
D/dx(eāæ)
Eāæ derivative of n
ā«Cosx
-Sinx
ā«-sinx
Cosx
ā«SecĀ²x
Tanx
ā«-cscĀ²x
Cotx
ā«Secxtanx
Secx
ā«-cscxcotx
Cscx
ā«1/n
Ln(n)
ā«Eāæ
Eāæ
When doing integrals never forget
Constant (+c)
ā«Axāæ
A/n+1(xāæāŗĀ¹)+C
ā«Tanx
Ln|secx|+c
-Ln|cosx|+c
ā«Secx
Ln|secx+tanx|+c
D/dx(sinā»Ā¹x)
1/ā1-xĀ²
D/dx(cosā»Ā¹x)
-1/ā1-xĀ²
D/dx(tanā»Ā¹x)
1/1+xĀ²
D/dx(cotā»Ā¹x)
-1/1+xĀ²
With derivative inverses
You plug in the number of the trigonometric function into x
D/dx(secā»Ā¹x)
1/|x|āxĀ²-1
D/dx(cscā»Ā¹x)
-1/|x|āxĀ²-1
D/dx(aāæ)
aāæln(a)
D/dx(Logāx)
1/xln(a)
Chain Rule
Take derivative of outside of parenthesis
Take derivative of inside parenthesis and keep the original of what was in the parenthesis
For example, sin(xĀ²+1)ā 2xcos(xĀ²+1)
Product Rule
d/dx first times second + first times d/dx second
Quotient Rule
LoDHi-HiDLo/LoLo
Fundamental Theorem of Calculus
ā«(a to b) f(x) dx = F(b) - F(a)
Basically saying that Fā(x)=f(x)
fĀ relativeĀ maxāf āĀ goesĀ from
Positive to negative
fĀ relativeĀ mināf āĀ goesĀ from
Negative to positive