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Universities » Notre Dame (ND) » MATH - Mathematics » 10350 - Calculus A » Flash Cards

Derivatives and Trig Functions - Flashcards

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Class:MATH 10350 - Calculus A
Subject:Mathematics
University:Notre Dame
Term:Fall 2010
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What is the derivative of sin x? cos x
What is the derivative of cos x? -sin x
What is the derivative of tan x? sec2 x
What is the derivative of sec x? sec x * tan x
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What is the derivative of csc x? -csc x * cot x
What is the derivative of cot x? -csc2 x
What is the Chain Rule for finding the derivative of functions f(g(x))`? f ` (g(x)) * g `(x)
How do you find the derivative using the General Power Rule? g(x)^n = n(g(x))^n-1 * g `(x) or e^g(x) = g `(x)*e^(g(x))
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How do you find the derivative of a function using the Shifting/Scaling Rule? f (kx + b) = k * f `(kx + b) or e^ (kx + b) = k * e^ (kx + b)
What are the steps to finding an equation of a tangent line? 1. Find the derivative of the given function 2. Plug in the given value for x 3. Result is the slope of the line 4. If necessary, put in points for x and y to solve for b. 5. If in point-slope form, #4 is unnecessary.
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 What is the derivative of sin x?cos x
 What is the derivative of cos x?-sin x
 What is the derivative of tan x?sec2 x
 What is the derivative of sec x?sec x * tan x
 What is the derivative of csc x?-csc x * cot x
 What is the derivative of cot x?-csc2 x
 What is the Chain Rule for finding the derivative of functions f(g(x))`?f ` (g(x)) * g `(x)
 How do you find the derivative using the General Power Rule?g(x)^n = n(g(x))^n-1 * g `(x)

or

e^g(x) = g `(x)*e^(g(x))
 How do you find the derivative of a function using the Shifting/Scaling Rule?f (kx + b) = k * f `(kx + b)

or

e^ (kx + b) = k * e^ (kx + b)
 What are the steps to finding an equation of a tangent line?1. Find the derivative of the given function
2. Plug in the given value for x
3. Result is the slope of the line
4. If necessary, put in points for x and y to solve for b.
5. If in point-slope form, #4 is unnecessary.
  Definition
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