how should i do this ...

**sedam7** · September 22nd 2010, 01:46 PM

i'm having problems when needed to show stuff like this ... i don't have problems applying those rules to solve some concrete problems (calculating them) but with this i'm clueless

so any help would be greatly grateful

i need to do... if for the function $f: \mathbb{R} ^n \to \mathbb{R}$ we put $g(t) = f(t,x_2, . . . , x_n)$ show that $g'(t) = D_{e_1} f(x_1,x_2, . . . , x_n)$

**Defunkt** · September 23rd 2010, 01:28 AM

$\displaystyle g'(t) = \lim_{h \to 0} \frac{f(t+h,x_2, \ldots , x_n) - f(t,x_2, \ldots , x_n)}{h}$

**HallsofIvy** · September 23rd 2010, 04:21 AM

Originally Posted by sedam7

i'm having problems when needed to show stuff like this ... i don't have problems applying those rules to solve some concrete problems (calculating them) but with this i'm clueless

so any help would be greatly grateful

i need to do... if for the function $f: \mathbb{R} ^n \to \mathbb{R}$ we put $g(t) = f(t,x_2, . . . , x_n)$

This is only saying that all "variables" except the first are held constant. Taking the derivative with respect to only one variable while keeping all others constant is just the "partial derivative" with respect to that variable and that is exactly what the conclusion says. For a formal proof do what Defunkt suggests.

show that $g'(t) = D_{e_1} f(x_1,x_2, . . . , x_n)$

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