2
votes
0answers
22 views

Rendering the derivative of composite functions from a graph

I'm on a workbook problem and I want to make sure I'm doing it properly. The problem asks me to find the derivatives of composite functions when given only the graphs of the original functions, here ...
1
vote
3answers
30 views

Notation for function compositions/derivatives

When given $(f \circ g)'(0)$, does it mean to compose the 2 functions first, then take the derivative of the composed functions and evaluate it at $0$, or take the derivative of $g$ first and evaluate ...
2
votes
0answers
38 views

Differentiablilty of composition functions

Two questions I suppose. One comes from a test I recently took that I didn't quite get/understand the method I should be using (or even how I should proceed) Let $f:R^2 \rightarrow R$ s.t $f$ is an ...
1
vote
1answer
135 views

A question about the composite function of a derivative

This may seem dumb, but, I'm trying to understand the proof of the chain rule, but here is my issue: By definition, the derivative is the following: $f'(a)=\lim\limits_{x\rightarrow ...
1
vote
3answers
124 views

$g(\theta):= f(\theta {\bf y} + (1 − \theta){\bf x})$, find $g'$.

Let $f: \mathbb{R}^n \longrightarrow \mathbb{R}$ and let $g: \mathbb{R} \longrightarrow \mathbb{R}$ given by $g(\theta):= f(\theta {\bf y} + (1 − \theta){\bf x})$. I want to calculate the derivative ...
0
votes
3answers
34 views

Derivatives of Functions

Suppose $ F(x)=f(g(x)) $ $g(1)=3$ $g'(1)=4$ $f'(1)=6$ $f'(3)=5$ What is $F'(1)$ ?
0
votes
1answer
192 views

Estimates of the norm of a derivative of a vector vector field composition

I would like to know one estimate of the euclidian norm of a derivative of a vector field composition. For example: Let $f:\mathbb R^n \to \mathbb R^m$ and $g:\mathbb R^p \to \mathbb R^n$ be two ...