Solve Calculus Problem: f'(x)g'(x) = xf'(x)+f(x) | 10th Fri

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The discussion focuses on solving a calculus problem involving the derivative of the function g(x) = xf(x). Participants are asked to use the definition of a derivative to demonstrate that g'(x) equals xf'(x) + f(x). The definition of a derivative is provided to guide the solution process. The urgency of the request is emphasized, with a deadline set for Friday the 10th. The original poster expresses gratitude for any assistance received in solving the problem.
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If you can work this out please try and reply to it before friday the 10th!



#1: If f is a differentiable function and g(x) = xf(x), use the
definition of a derivative to show that g'(x)(g prime of x) =
xf'(x)+f(x)(xf prime of x plus f of x).

Definition of a Derivative:

The Derivative of a function f at a number a, denoted by
f'(a) (f prime of a), is:

Lim f(a + h) - f(a)
x -> 0 --------------
h​
 
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Apply the definition directly to g(x).
 
Thanks a lot, I found/got the right answer
 

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