deiluefniwf

2022-09-23

Let B be a matrix $m×n$. Let $b\in {\mathbb{R}}^{m}$. Let $f:{\mathbb{R}}^{n}\to {\mathbb{R}}^{m}$ be the function defined as $f\left(x\right)=Bx+b$
What is the Df(x)(derivative) and how can I find it from the derivative definition?

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Amiya Watkins

Expert

$\begin{array}{r}Df\left(x\right)=\underset{h\to 0}{lim}\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{B\left(x+h\right)+b-Bx-b}{h}=\frac{Bh}{h}=B\end{array}$

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