Studied by 21 peopleCalculus
Derivatives & Differentiation
AP Calculus AB
Unit 2: Differentiation: Definition and Fundamental Properties
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Addition Rule (f + g)
f’ + g’
Subtraction Rule (f - g)
f’ - g’
Multiplication Rule (fg)
f’g + fg’
Division Rule (f / g)
(f’g - fg’) / (g²)
Power Rule (f(x) = x^n)
nx^(n-1)
Constant Rule (f(x) = c)
f’ = 0
Constant Multiple Rule (f(x) = cx)
f’ = c
Derivative of sin(x)
cos x
Derivative of cos(x)
-sin x
Derivative of tan(x)
sec²x
Derivative of cot(x)
-csc²x
Derivative of sec(x)
(tan x)(sec x)
Derivative of csc(x)
-(cot x)(csc x)
Exponential Rule (f(x) = a^x)
(a^x)(ln a)
Derivative of e^x (f(x) = e^x)
e^x
Logarithm Rule (f(x) = log_a(x))
1 / (x)(ln a)
Natural Logarithm Rule (f(x) = ln x)
1/x
Chain Rule (f(g(x)))
f’(g(x))*g’(x)
sin^-1(x)
1 / sqrt(1 - x²)
sec^-1(x)
1 / |x|*sqrt(x² - 1)
tan^-1(x)
1 / (x² + 1)
cos^-1(x)
-1 / sqrt(1 - x²)
csc^-1(x)
-1 / |x|*sqrt(x² - 1)
cot^-1(x)
-1 / (x² + 1)
Function Inverse Derivative (f^-1(x))
1 / f’(f^-1(x))
Note
Flashcard