# Section 3.2 - object as a funciton of time t is called a...

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Basic Differentiation Rules and Rates of Change

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The Constant Rule The derivative of a constant function is 0. In other words, if c is a real number, then [ ] 0 = c dx d
The Power Rule: If n is a rational number, then the function is differentiable and (be careful at x=0) The Constant Multiple Rule: (if f is a differentiable function.) [ ] 1 - = n n nx x dx d n x x f = ) ( ) ( ' )] ( [ x cf x cf dx d =

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The Sum and Difference Rules If f and g are differentiable, then their sum and difference are also differentiable. Furthermore, [ ] x x e e dx d = [ ] ) ( ' ) ( ' ) ( ) ( x g x f x g x f dx d ± = ±
Trig and Exponential Derivatives [ ] x x dx d cos sin = [ ] x x dx d sin cos - = [ ] x x e e dx d =

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A function s that gives position (relative to the origin) of an

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Unformatted text preview: object as a funciton of time t is called a position funciton. Average velocity = distance / time For a position function s(t), the average velocity over the time interval [t,t+h] is h t s h t s ) ( ) (-+ To find instantaneous velocity, what should we do to the length of the time interval? Make it approach zero Example: • #94 • A ball is thrown straight down from the top of a 220-foot building with an initial velocity of – 22 feet per second. What is its velocity after 3 seconds? What is its velocity after falling 108 feet?...
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Section 3.2 - object as a funciton of time t is called a...

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