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 December 30th, 2011, 01:44 AM #1 Member   Joined: Aug 2011 Posts: 78 Thanks: 0 The value of g in the gradient formula Hello, But of a dull question really but it does not care to explain in the book I have, the value of g in this formula: if y=f(x)± g(x) then dy/dx=f'(x)±g'(x) thanks
 December 30th, 2011, 01:52 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,932 Thanks: 1127 Math Focus: Elementary mathematics and beyond Re: The value of g in the gradient formula The derivative of the sum is the sum of the derivatives. g is a function of x. Example: y = 2x² + x³, f(x) = 2x², f'(x) = 4x, g(x) = x³, g'(x) = 3x², dy/dx = 4x + 3x².
December 30th, 2011, 02:00 AM   #3
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Re: The value of g in the gradient formula

Quote:
 Originally Posted by greg1313 The derivative of the sum is the sum of the derivatives. g is a function of x. Example: y = 2x² + x³, f(x) = 2x², f'(x) = 4x, g(x) = x³, g'(x) = 3x², dy/dx = 4x + 3x².
cheers greg is a constant or can it be any value?

December 30th, 2011, 02:01 AM   #4
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Re: The value of g in the gradient formula

From another forum:

Quote:
 Differentiation is a linear transformation for the vector space of differentiable functions over the field of reals.
We may write:

$\frac{d}{dx}$$f(x)\pm g(x)$$=\lim_{\Delta x\to 0}\frac{$$f\(x+\Delta x$$-f(x)\)\pm$$g\(x+\Delta x$$-g(x)\)}{\Delta x}=$

$\lim_{\Delta x\to 0}\frac{f$$x+\Delta x$$-f(x)}{\Delta x}\pm\lim_{\Delta x\to 0}\frac{g$$x+\Delta x$$-g(x)}{\Delta x}=$

$\frac{df}{dx}\pm\frac{dg}{dx}$

December 30th, 2011, 02:14 AM   #5
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Re: The value of g in the gradient formula

Quote:
 Originally Posted by dthomas86 is a constant or can it be any value?
Generally, g is a function of x, and its value depends on x.

It may be a constant function, in which case it will be the same value regardless of the value of x; e.g: g(x) = 3, g'(x) = 0.

It may be a rational function, e.g: g(x) = (x² + 2)/(x³ - 1), which is undefined for x = 1.

etc.

 December 30th, 2011, 03:21 AM #6 Member   Joined: Aug 2011 Posts: 78 Thanks: 0 Re: The value of g in the gradient formula thanks again I love this forum people are so helpful!

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