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Quotient and Product Rule
Back to the Basics
Chain Rule
Derivative Rules
Think Like a Mathematician
100
Take the derivative. (x-1)/(x+1)
-2/(x+1)^2
100
What is the limit of (2x+4) as x approaches from the left?
6
100
Take the derivative. (x-1)^2
x-1
100
What is the power rule?
(x^n)' = nx^(n-1)
100
If Pagans are sun worshipers, what are mathematicians?
Sum worshipers.
200
Take the derivative. (x^2 - 4x)*(5x^3 + 1)
(2x - 4)(5x^3 + 1) + (15x^3)(x^2 - 4x)
200
What is the limit of (1/x) as x approaches 0 from the right?
Negative infinity
200
Take the derivative. (x^2 - 4x + 1)^3
(2x-4)*2*(x^2 - 4x + 1)^2
200
What is the derivative of e^x and lnx?
e^x and 1/x
200
What does the zero say to the infinity?
Nice belt.
300
Take the derivative using the quotient rule. (14x - 1)/(x^2)
(14 - 28x^2 - 14x)/(x^4)
300
What are the three rules to continuity? (check your book or notes)
1) f(a) is exists. 2) lim f(x) as x approaches a exists. 3) lim f(x) as x approaches a is equal to f(a)
300
Take the derivative. (x^2 + 5 - lnx)^2
(2x -1/x)*2*(x^2 + 5 - lnx)
300
What is the product rule?
[f(x)*g(x)]' = g(x)*f'(x) + f(x)*g'(x)
300
What's the difference between a PhD in mathematics and a pizza?
A pizza can feed a family of four.
400
Take the derivative using the product rule. (e^x^2)(lnx)
(e^x^2)/x + (2xe^x^2)(lnx)
400
Where is the following function not continuous? f(x) = (x+1)/(x-1)
When x = 1
400
Take the derivative. [f(x)*g(x)]^3
3*[f'(x)g(x) + g'(x)f(x)]*[f(x)*g(x)]^2
400
What is the quotient rule?
[f(x)/g(x)]' = [g(x)*f'(x) - f(x)*g'(x)]/(g(x)^2)
400
What's the first derivative of a cow?
Prime rib.
500
Find the second derivative of the following. (x^2)(lnx)
2lnx + 3
500
Take the derivative of the following function using the original limit based derivative method. 2x^2 + 4x - 2
4x + 4
500
Take the derivative. (e^x^3 + lnx)^4
[(3x^2)(e^x^3) + 1/x]*4*(e^x^3 + lnx)^3
500
What is the chain rule?
[f(x)^n]' = f'(x)*n*[f(x)^(n-1)]
500
What does the little mermaid wear?
An algae-bra.