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1
Use derivatives to identify global extrema
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2
Compute the derivative of functions involving logarithmic functions
dxd[cos(x)]=-sin(x)
dxd[sin(x)]=cos(x)
dxd[tan(x)]=sec2(x)
3
Identify and interpret local extrema of a function using a graph and using derivatives
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4
Compute the derivative of functions using inverse trigonometric
dxd[sin(x)]=cos(x)
dxd[cos(x)]=-sin(x)
dxd[tan(x)]=sec2(x)
5
Compute the derivative of functions using combinations of rules and functions
Put the rules in alphabetical order
Apply the rules in reverse order
Use any rule you feel like in any order
Apply the appropriate rules in the correct order.
6
Compute the derivative correctly for products, quotients, and composites
Use the product rule, quotient rule, and chain rule respectively.
Use only the quotient rule
Use only the product rule
Use the sum rule
7
Power Rule
If f(x) = n^x then derivative is f'(x) = n - x^(n-1)
If f(x) = n^x then derivative is f'(x) = n * x^(n-1)
If f(x) = n^x then derivative is f'(x) = n + x^(n-1)
If f(x) = n^x then derivative is f'(x) = n * x^(n-2)
8
Understand f(x)'s in context, estimate values using difference quotients, and make predictions with derivatives.
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9
Identify and interpret concavity of a function using a graph and using derivatives.
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10
Constant Multiple Rule
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11
Use derivatives to model and solve applied optimization problems
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12
Compute the derivative involving trigonometric
dxd[tan(x)]=sec2(x)
dxd[sin(x)]=cos(x)
dxd[cos(x)]=-sin(x)
13
Use the Fundamental Theorem of Calculus to evaluate definite integrals
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14
Set up and solve using implicit differentiation a related rates problem
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15
Sum Rule
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16
Interpret the meaning of a definite integral by estimating and calculating it geometrically
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17
The derivative of a constant is
3
2
0
1
18
Compute derivatives accurately for power, exponential, sine, cosine, sum, constant multiple, and constant functions
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19
The constant multiple rule is used when differentiating a function that is the product of a constant and a function
True
False
20
Determine where d/dx is continuous or differentiable given a graph or formula of the function and explain your reasoning
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21
Find the derivative of an implicitly defined function and use it to determine the tangent line at a point.
Take one side with respect to y and the other side with respect to x
Apply the chain rule to one side of the equation, then integrate both sides
Divide both sides of the equation by "x" and then take the derivative
Diff. both sides of the equation with respect to x, then solve for dy/dx
22
If f(x) = n^x then derivative is f'(x) = n * x^(n-1)
False
True
23
Sum rule is used to find the derivative of the sum of one function
True
False
24
Exponential Rule (a^x)
d/dx a+x = a^x ln(a)
d/dx a^x = a^x ln(a)
d/dx a-x =a^x ln(a)
d/dx a*x = a^x ln(a)
