Unit 9 Math Test Flashcards
Derivative of a constant function
0
Power Rule
n * x^n-1
Sum and Difference Rule
f’(x) + g’(x)
Product Rule
f’(x)g(x) + f(x)g’(x)
Quotient Rule
(Low di Hi - Hi di Low)/Low^2
Chain Rule
O’(I) * I’
Second Derivative
y^n
Third Derivative
y^m
f(x) = b^x
f’(x) = b^x * ln(b)
f(x) = e^x
f’(x) = e^x
f(x) = logb(x)
f’(x) = 1/(xln(b))
What is a derivative?
An instantaneous rate of change. The slope of the tangent line.
Slope of the Secant Line
Slope formula
“Find the instantaneous rate of change”
lim Q->p f(x2) - f(x1)/ x2-x1
“Write the equation of the line tangent to”
Point-slope form
y - y1 = m(x - x1)
Definition of Derivative (equation)
f’(x) = lim -> 0 f(x+h) - f(x) / h
If you’re finding a derivative from a point
DON’T USE THE H DEFINITION
When is a point differentiable?
A point (a, f(a)) is differentiable if it has a derivative at x = a
Name the four cases where a function is not differentiable
- Corner: f(x) = |x| at x = 0
- Cusp: f(x) = x^2/3 at x = 0
- Vertical Tangent: f(x) = cubed(x) at x = 0
- Discontinuity
What is the relationship between differentiable and continuous functions?
is f(x) is differentiable at x = a then it is continuous at x = a
f(x) = ln(x)
f’(x) = 1/x
d/dx[f^-1(x)]
1/f’(f^-1(x))
