6. The Derivative Flashcards
1
Q
Parameterisation of line.
Restriction of function to line.
A
2
Q
Definition 6.1
Directional derivative.
A
3
Q
Definition 6.4
Differentiable.
Frechet derivative.
best affine linear approximation
A
4
Q
Proposition 6.7
Differentiability implies…
A
5
Q
Exercise 6.2
f : U -> R^k is differentiable at x \in U iff.
A
6
Q
Proposition 6.9
If Df(x) exists then…
If f is differentiable at x then…
A
7
Q
Definition 6.11
i-th partial derivative.
A
8
Q
Definition 6.12
Jacobian matrix
A
9
Q
Definition 6.13
Gradient of f at x
A
10
Q
Proposition 6.15
If f : U -> R^k is diff. at x \in U and h \in R^n…
A
11
Q
Theorem 6.23
Chain rule
A
12
Q
Theorem 6.30
if f : U -> R^k and B(x,r) \subset U st \partial f(y) exists…
A
13
Q
Definition 6.32
Continuously differentiable.
A
