Derivative Rules
u'v+uv'
What is the Product Rule?
-sin(x)
What is the derivative of cos(x)?
It shows the slopes of the tangent lines at any point on the original curve.
What does the graph of the derivative describe? or What is the graph of the derivative?
The limit as x approaches 2 of (x2+1).
What is 5?
'Pebbles' or 'Small stones'
What does Calculus mean in Latin?
(u'v-uv') / (v2)
What is the Quotient Rule?
sec2(x)
What is the derivative of tan(x)?
A local maximum, a local minimum, or a critical point.
What does it mean when f'(x)=0?
Acceleration is the physical description that relates by differentiation to these two other physical descriptions.
What are velocity and position?
The Grinch is as cuddly as a ________.
What is a cactus?
f'(g(x)) * g'(x)
What is the Chain Rule?
-cot(x) * csc(x)
What is the derivative of csc(x)?
The second derivative will change signs (pos to neg, or vice versa) at this point.
How do you decide whether a critical point is an inflection point?
This amazing derivative is exactly proportional to itself!
What is the derivative of ex?
Isaac Newton. It is a nickname for one of the primary founders of Calculus.
Who is the Father of Calculus?
bx * ln(b)
What is the derivative of bx?
1 / (1+x2)
What is the derivative of arctan(x)?
This is true of f when f''(x)>0.
When will the original graph, f(x), be concave up?
A discontinuity caused by a factor that cancels.
What is a removable discontinuity?
Ecclesiastes 3:9-14
"What gain has the worker from his toil? I have seen the business that God has given to the children of man to be busy with. He has made everything beautiful in its time. Also, he has put eternity into man's heart, yet so that he cannot find out what God has done from the beginning to the end. I perceived that there is nothing better for them than to be joyful and to do good as long as they live; also that everyone should eat and drink and take pleasure in all his toil—this is God's gift to man. I perceived that whatever God does endures forever; nothing can be added to it, nor anything taken from it. God has done it, so that people fear before him."
1 / (xln(b))
What is the derivative of logbx?
1 / (|x| * (x2-1)1/2)
What is the derivative of arcsec(x)?
There are a few instances when this happens, including when f'(x) or f''(x) is concave up/down and when f''(x) is increasing/decreasing.
When do the graphs of derivatives NOT communicate anything about the original function?
These are three conditions required for a function to be continuous at x=c.
2.) The limit as x approaches c exists.
3.) The limit as x approaches c equals f(c).
Green
What is Mr. Hatting's favorite color?