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!