Derivatives Derivatives By: Josh Hansen Brady Thompson Rex McArthur.
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Transcript of Derivatives Derivatives By: Josh Hansen Brady Thompson Rex McArthur.
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Derivatives
By: Josh Hansen Brady Thompson Rex McArthur
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Slope
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Definition of a DerivativeDefinition. Let y = f(x) be a
function. The derivative of f is the function whose value at x is the limit
provided this limit exists. If this limit exists for each x in an
open interval I, then we say that f is differentiable on I.
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Example
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Shortcut for derivatives
1n ndx nx
dx
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Examples
4f x x 34f x x
8y x 78y x
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A= -cos(2x)
B= 2cos(2x)
C=-4sin(2x)
D= -4cos(2x)
Answer is CA- forgot to do
the chain ruleB- only took the
first derivativeD- wrong trig
function
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what is the derivative of sin(5x3 + 2x) ?
sin(5x3 + 2x) ?◦ A= cos(5x^3+2x)
◦ B= cos(5x^3 + 2x) * (15x^2 + 2)
◦ C= sin(5x^3 + 2x) * (15x^2+2)
◦ D= 0
The answer is BA no chain ruleC wrong functionD wrong in every
way
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What is the Derivative of F(x) = 12X^2+12x+4A-4x^3 + 6x^2
+ 4xB- no solutionC-12x+12D-24x+12
Answer is DA is anti-
derivative B is Really Wrong
C they forgot to bring down the 2
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FindProduct Rulehttp://calc101.com/
product_rule_2.html
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Free ResponseWhat is the derivative of (4X3 +
5X2 -7X +10)14 ?
http://www.1728.com/chainrul.htm
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Where the derivative fails to exist Corner
Cusp
Vertical Tangent
Discontinuity
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Don’t forget the chain rule
Multiply by the derivative of the inside
Find the derivative of
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Website to help studentshttp://www.wolframalpha.com/ex
amples/Calculus.htmlExample from website
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Example 1:
For a circle:
2A r
2dA dr
dr dr
2dA
rdr
Instantaneous rate of change of the area withrespect to the radius.
For cookie growth, if the change in area is constant then dr must get smaller as r gets larger.
2 dA r dr
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SEE ALSO: Blancmange Function, Calculus, Carathéodory Derivative, Cauchy-Riemann Equations, Chain Rule,
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Q: What is the first derivative of a cow?
A: Prime Rib!