12-02: Derivatives
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21 Terms
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chain rule
The ________ is an effective way of differentiating a composite function by first: differentiating the outer function with respect to the inner function, then multiplying by the derivative of the function.
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Distance
________ and direction that an object has moved from an origin over a period of time.
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Velocity
________: a vector quantity with both magnitude and direction.
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IROC
a derivative
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To differentiate radicals
express it as a power with a rational exponent
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To differentiate a power of x that is in the denominator
express as a power with a negative exponent
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Use y=mx+b, plug in (x,y) from tangent point and slope
isolate for b
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Composite function
one function being subbed into another function
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The chain rule is an effective way of differentiating a composite function by first
differentiating the outer function with respect to the inner function, then multiplying by the derivative of the function
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Second derivative
f(x) determined by differentiating the first derivative (same process, just starting from the first derivative)
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Speed
a quantity or scale that describes the magnitude of motion but does not describe direction
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Velocity
a vector quantity with both magnitude and direction
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Answer for velocity questions can be either + or
and the sign indicates the direction at which the object is travelling
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when v(t) = 0
object is at rest
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when v(t) > 0
object is moving in a + direction
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when a(t) > 0
object is accelerating; velocity is increasing
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when a(t) < 0
object is decelerating; velocity is decreasing
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if v(t) a(t) > 0
object is speeding up
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if v(t) a(t) > 0
object is slowing down
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Second derivative
f’’(x) determined by differentiating the first derivative (same process, just starting from the first derivative)
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Possible speed and acceleration values
when v(t) = 0: object is at rest
when v(t) > 0: object is moving in a + direction
when v(t) < 0: object is moving in a - direction
when a(t) > 0: object is accelerating; velocity is increasing
when a(t) < 0: object is decelerating; velocity is decreasing
if v(t) • a(t) > 0: object is speeding up
if v(t) • a(t) > 0: object is slowing down
when v(t) > 0: object is moving in a + direction
when v(t) < 0: object is moving in a - direction
when a(t) > 0: object is accelerating; velocity is increasing
when a(t) < 0: object is decelerating; velocity is decreasing
if v(t) • a(t) > 0: object is speeding up
if v(t) • a(t) > 0: object is slowing down