Derivative Rules Flashcards
Quotient Rule Phrase
low d high minus high d low, square the bottom and off we go
f(x)= mx^(n)
f’(x)= mnx^(n-1)
Derivative Notation
f’(x) y’ (dy)/(dx) (df(x))/(dx) d/(dx)
Product rule
f’(x)= f’g + g’f
Quotient rule
(gf’ -fg’)/g²
Differentiability
Must be continuous at x=c and left-hand derivative= right-hand derivative
Derivative definition
Slope of the tangent line at a point
f(g(x))
f’(g(x)) × g’(x)
Average rate of change
2 places (Δy/Δx)
Instantaneous Rate of Change
Derivative of function
Matching Graphs of Functions
if graph 1 is f(x), then graph 2 of f’(x) will have x-intercepts at all relative extrema (max’s and min’s)
Piecewise Functions (both differentiable and continuous)
- Plug in x-values and set original equations equal too each other
- Take derivatives of equations and set equal to each other (then plug in x-value)
- Set up a system of equations
Piecewise Functions (just continuous)
- Plug in x-values and set equations equal to each other (repeat if more than 2 equations)
- Set up a system of equations
Find points where horizontal or vertical tangent line
f’(x) = a/ b
1. Horizontal is set a = 0
2. Vertical is set b = 0
Average ROC
slope of secant line