Calculus Unit 2 Derivatives Overview
Terms in this set (...)
Formula for the Derivative by the Limit Process
The formula for the deriative by the limit process comes from...
The tangent line problem
y - y₁=m(x - x₁)
If an equation is NOT continuous, then it is ____ _________.
If an equation has a sharp turn, then it is _____ ____________.
If an equation has a vertical tangent line, then it is ______ ______________
An equation must be ______________ to be differentiable, but being _____________ does not guarantee differentiablility.
A derivative is a graph of the ___________ of the _________ line at each point.
d/dx means taking the derivative with _________ to ____.
The derivative of a constant is always = _____
Sum Rule: d/dx[f(x) + g(x)]=
f'(x) + g'(x)
Difference Rule: d/dx[f(x) - g(x)]=
f'(x) - g'(x)
Power Rule: d/dx[ xⁿ]=
You can only use the power rule when the variable is in the _____________
You can only use the power rule when there are NOT ________ NOR _________ of variables
You can only use the power rule when there are NOT _________ outside a parenthesis that would cause a variable to have a higher degree
The derivative of position is
The derivative of velocity is
s(t) usually represents
s'(t) usually represents
s''(t) usually represents
Initial velocity (starting velocity)
Initial height (starting height)
Product Rule (Mnemonic)
Quotient Rule (Mnemonic)
LowDHi-HiDLow over the square of what's below
f'''(x) means the third derivative. We use tick marks to represent the level of all derivatives up to the third derivative. But how do we write the fourth derivative?
Chain Rule: d/dx[f(u)]=
Chain Rule: d/dx[f(g(x))]=
Never leave answers with _________ exponents
Never leave answers with _________ fractions
The chain rule states that if you take the derivative of the outside, and the inside is differentiable, then you have to multiply by the ________ of the __________
Explicit Form means that the equation is in terms of _____
Implicit Form means that there are x's and y's on the _______ _______ of an equation.
As you take a derivative of y with respect to x, you have to multiply the derivative by ________
In implicit differentiation, we multiply by dy/dx because of the _________ rule
d²y/dx² means to find the __________ ____________
Most of the problems in chapter 2 will use a combination of the power rule, along with these 3 rules.
Product Rule, Quotient Rule, Chain Rule
If a graph of an equation has a horizontal tangent line (slope of zero), then the graph of its derivative should cross the ___-_______ at that point
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