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**thaopanda** Let f : $\displaystyle R^3 \rightarrow R^2$ be given by f ($\displaystyle x_1, x_2, x_3$) = ($\displaystyle x_3, x_1$). Show that f is differentiable at $\displaystyle X_0$ = (0,0,0) and find df($\displaystyle X_0$).

I figured to use the definition so:

f(X) = f($\displaystyle X_0$) + df($\displaystyle X_0$)(X-$\displaystyle X_0$) + o(|x-$\displaystyle X_0$|) as X $\displaystyle \rightarrow X_0$

f($\displaystyle X_0$) goes to 0 and X-$\displaystyle X_0$ is just X

So I'm left with:

f(X) = df($\displaystyle X_0$)(X) + o(|X|) as X $\displaystyle \rightarrow X_0$

But I'm not sure how to find df($\displaystyle X_0$)

Doing so would that f is differentiable at $\displaystyle X_0$ and find it at the same time, yes?