Implicit Differentiation
Would the following require implicit differentiation? Differentiate: x + y = 0
Yes
Identify the meaning of the following: f(x)= 3x^2, what is 2f’(x) + f”(x) - f(x)
12x+6-3x^2
What do you do if you have 2 unknown variables within a formula that you are trying to take the derivative of?
Use geometry to eliminate one of the variables
What is the “Golden Rule” of implicitly differentiation
Put Dy/dx after differentiating y
When do you plug in the denominator = 0?
To find the vertical tangent
What unit should angles be converted to in a related rate problem?
Radians
Differentiate: y = sin(x + y). Leave y’
cos(x + y)(1 + y')
What is the derivative of 2xy^3+ 4x = 0
Dy/dx = -4/6xy^2
What are the units of the IRC of water in respect to with a problem involving a right cone over time t?
V/t
Under what type of situation would you use implicit differentiation on both x and y?
On related rate problems
Find the horizontal tangents of the following function: 2y + 4x^2 +4x = 0
X= + or - 1/2
What can related rates be used for to maximize total area and other aspects of a certain structure/system?
Optimization
If I were to ask you to solve for x', how would you express this in terms of Leibniz Notation?
dx/dy
How do you tell if a function has a cusp or node?
If the numerator and denominator = 0
What geometrical principle is usually used in related rate problems to eliminate a variable?
similarity