Chapter 3- Differentiation Flashcards
0
Q
Differentiable
A
If limit exists
We say that f is differentiable at x = a
1
Q
Derivative of f(a)
A
f(a + h) - f(a) f(x) - f(a)
lim —————– = lim ————–
h->0 h x-> a x - a
2
Q
Tangent line in point-slope form
A
y - f(a) = f’(a) (x-a)
3
Q
To calculate f’(a) using the limit definition
A
- Write out the numerator of the difference quotient
- Divide by h and simplify
- Compute the derivative by taking the limit
4
Q
Power rule
A
d
— x^n = nx^(n-1)
dx
5
Q
Sum rule
A
(f + g)’ = f’ + g’
6
Q
Constant multiple rule
A
(cf)’ = cf’
7
Q
d
— e^x
dx
A
e^x
8
Q
Differentiability implies continuity
A
However, there exist continuous functions that aren’t differentiable
