Date post: | 19-Jan-2016 |
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Derivatives
By: Josh Hansen Brady Thompson Rex McArthur
Slope
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.
Example
Shortcut for derivatives
1n ndx nx
dx
Examples
4f x x 34f x x
8y x 78y x
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
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
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
FindProduct Rulehttp://calc101.com/
product_rule_2.html
Free ResponseWhat is the derivative of (4X3 +
5X2 -7X +10)14 ?
http://www.1728.com/chainrul.htm
Where the derivative fails to exist Corner
Cusp
Vertical Tangent
Discontinuity
Don’t forget the chain rule
Multiply by the derivative of the inside
Find the derivative of
Website to help studentshttp://www.wolframalpha.com/ex
amples/Calculus.htmlExample from website
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
SEE ALSO: Blancmange Function, Calculus, Carathéodory Derivative, Cauchy-Riemann Equations, Chain Rule,
Q: What is the first derivative of a cow?
A: Prime Rib!