Derivative Rules
What is the product rule?
f'g+g'f
Derivative of sinx
cosx
What does the graph of the derivative describe?
It shows all the slopes of lines tangent to the original graph
For f(x)= 2x3-3x2-12x+18, the graph decreasing and concave up over the interval (-1, .5). What is true about the first and second derivatives?
The first derivative is negative and the second derivative is positive.
What is the name of that guy who made the rule about limits that are 0/0
l'hopital
What is the quotient rule?
f'g-g'f/ g2
Derivative of tanx
sec2x or 1/cos2x
What does it mean when f'(x)= 0
A maximum, minimum, or critical point
If f(x)= x2-4, and g is a differentiable function of x, what is the derivative of f(g(x))
2g'(x)
What does calculus mean in latin?
small stone
What is the derivative of ax?
(ax ) ln(a)
Derivative of cscx
-cscxcotx or -cosx/sin2x
How do you decided whether a critical point is a maximum or minimum?
Positive to negative = max; negative to positive =min
Differentiate: 3sin(5x^2)
(ln3)3sin(5x^2)cos(5x^2)10x
What is Mr. Hernandez's favorite hobby?
Pickleball
What is the derivative of logax?
1/(xlna)
Derivative of tan-1x
1/(1+ x2)
What does it mean when f''(x)= 0
lim as x approaches 0 for (1 - cosx)/x2
1/2
Why is the derivative of x equal to 1?
the line y=x, the slope is always one
Write the chain rule
f'(g(x))g'(x)
Derivative of csc-1x
1/ (lxl ((x2-1)1/2)
How do you figure out when the original graph, f(x), is concave up?
When f''(x)>0
The Mean Value theorem for derivatives
What is f'(x) = (f(b) - f(a))/(b - a)
Who is the real father of Calculus?
Newton or Leibniz - the debate will never end.