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December 30th, 2011, 01:44 AM   #1
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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
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December 30th, 2011, 01:52 AM   #2
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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 = 2x + x, f(x) = 2x, f'(x) = 4x, g(x) = x, g'(x) = 3x, dy/dx = 4x + 3x.
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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 = 2x + x, f(x) = 2x, f'(x) = 4x, g(x) = x, g'(x) = 3x, dy/dx = 4x + 3x.
cheers greg is a constant or can it be any value?
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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:





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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) = (x + 2)/(x - 1), which is undefined for x = 1.

etc.
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December 30th, 2011, 03:21 AM   #6
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Re: The value of g in the gradient formula

thanks again I love this forum people are so helpful!
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