Differentiate linear transformation

Question

Looking at the answer of this question:

I don't understand why if $T$ is linear then

$$(T\circ \gamma)'(t)=T\circ \gamma'(t)$$

I will appreciate any comment to help me to understand

score 2 · Accepted Answer · answered Mar 12 '17 at 15:29

2

This is an application of the chain rule together with the fact that for any linear transformation $T,\ T'(x)=T:$

$(T\circ \gamma)'(t)=T'(\gamma (t))(\gamma'(t))=T(\gamma '(t))=T\circ \gamma'(t).$

answered Mar 12 '17 at 15:29

Matematleta

How do you get the third equality? – user326159 Mar 12 '17 at 15:37
$T'(\gamma (t))=T$ since $T$ is linear and $T(\gamma '(t))=T\circ \gamma'(t)$ by def of composition. – Matematleta Mar 12 '17 at 15:47

1 Answers1