Let B be a matrix m xx n. Let b in RR^m. Let f:RR^n to RR^m be the function defined as f(x)=Bx+b. What is the Df(x)(derivative) and how can I find it from the derivative definition?

Jaydan Ball

Jaydan Ball

Open question

2022-08-21

Let B be a matrix m × n. Let b R m . Let f : R n R m be the function defined as f ( x ) = B x + b
What is the D f ( x ) (derivative) and how can I find it from the derivative definition?

Answer & Explanation

Ben Reese

Ben Reese

Beginner2022-08-22Added 12 answers

D f ( x ) = lim h 0 f ( x + h ) f ( x ) h = B ( x + h ) + b B x b h = B h h = B

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