# Vector Space Proof

• Jun 14th 2009, 10:15 AM
jusstjoe
Vector Space Proof
Let V denote the set of all differentiable real valued funtion defined on the real line. Prove that V is a VS under the operation of addition and scalar multiplication defined as follows:

I just don't know how to get started with this problem. I guess I'm having a problem thinking...what function are they talking about? How can you generalize all trig function, exponential function, polynomial into this? I don't know how to show the 8 axioms in this example. Like with the polynomials I know that i could define something like : anx^n+(An-1)X^n-1....AnX^1+An and then work with this, but I don't know how to proceed in the above.

Any help would be much appreciated.
• Jun 14th 2009, 10:23 AM
Plato
Quote:

Originally Posted by jusstjoe
Let V denote the set of all differentiable real valued funtion defined on the real line. Prove that V is a VS under the operation of addition and scalar multiplication defined as follows.

Is the derivative of a sum of two differentiable functions the sum of their derivatives?

Is the derivative of a scalar times a differentiable function that scalar times that function's derivative?