Need help on Chain Rule for multivariate function.

Question

I am given the function $S(t) = v\begin{pmatrix}t, 1-t, \frac{1}{1-t}\end{pmatrix}$. I need to find $S'(t)$ in terms of $t,\,v'_1,\,v'_2\,v'_3$. How do I do so?

I am thinking of the following:

$$ \begin{align*} S'(t) &= v'_1 +v'_2\dot{} -1 + v'_3\dot{}\frac{1}{(1-t)^2}\\&=v'_1-v'_2+\frac{v'_3}{(1-t)^2} \end{align*} $$

Any ideas if this sounds correct?

Is $v$ a function with three variables such that $\operatorname{im}(v)\subseteq \Bbb R^3$? — Git Gud, Mar 17 '13 at 16:54
Oh no, the question did not state...but since this is differentiation in real space, yes, $v$ is a function with 3 variables but they can be expressed in terms of 1 real variable $t$. of course, in this case $t \neq 1$ — bryan.blackbee, Mar 17 '13 at 17:04
hey, not sure if you know this, but if i post my own ans to my own qn, i can only accept them in 48 hours...i will follow up in due time. — bryan.blackbee, Mar 17 '13 at 18:51

score 2 · Accepted Answer · answered Mar 17 '13 at 17:16

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Thanks to the community, it has been verified as correct.

answered Mar 17 '13 at 17:16

bryan.blackbee

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Need help on Chain Rule for multivariate function.

1 Answers1