Basic Derivatives
The derivative of y = 3,123
What is 0?
The meaning of d/dx.
What is the derivative?
What is multiplication?
When two expressions are being ___________ we know to use the quotient rule.
What is division?
What a derivative represents on a graph.
What is the slope or rate of change?
The derivative of y = 3x2 - 20x
What is 6x - 20?
How you say "f'(x)."
What is "f prime of x"?
The first step of the product rule.
What is identify your f and g and find their derivatives?
The first step of the quotient rule.
What is identify your f and g and find their derivatives?
The process we can use to approximate instantaneous rate of change of a specific instant in time.
What is taking the average rate of change of two points close to that instant?
The derivative of 0.5x6 + 12x5 - 4x +100.
What is 3x5 + 60x4 - 4?
The name of the first derivative.
What is velocity?
The derivative of (3x5)(2x4).
What is 54x8?
The derivative of y = 2x2/10.
What is 40x/100 or 4x/10?
A cubic function turns into a _________ function when we take the derivative because the ________ rule tells us to subtract one from the exponent.
What is quadratic and power?
The derivative of g(x) when g(x) = 2f(x) and f(x) = 14x3 - 12x2 + 10x - 12,456.
What is 84x2 - 48x + 20?
The two other ways we say the derivative of something.
What is instantaneous rate of change or the slope of the tangent line?
The derivative of (2x3 + 5)(ex - 2).
What is 6x2ex - 12x2 + 2x3ex + 5ex?
The derivative of (9x2 - 5x)/(3x + 5).
What is (27x2 + 90x - 25)/(9x2 + 30x + 25)?
The derivative of ln(x) is ______ therefore we know that the ________ of the graph of ln(x) gets (smaller/bigger) as x increases.
The derivative of h(x) when h(x) = 3f(x) - 0.5g(x), f(x) = x4ex + 12x - 100, and g(x) = 4x4ex + 58x.
What is 4x3ex + 7?
The name of the fourth derivative.
What is snap or jounce?
The derivative of (12x3 - 3x2 + 7x)(15x4 + 2x2).
What is 1260x6 - 270x5 + 645x4 - 24x3 + 42x2?
The derivative of (7x3 - 1)/(ex + 300).
What is (21x2ex + 6300x2 - 7x3ex + ex)/(e2x + 600ex + 90,000)
When the _______ line approaches the _______ line, our __________ rate of change approaches our __________ rate of change.
secant, tangent, average, instantaneous