HELP PLEASE!
If f:R^2-R^3 and g:R^3-R and h = g◦f, h(uv)=g(f(u,v)) for every (u,v) E R^2.
How do you calculate derivative h/u in point (a,b)?

Question

HELP PLEASE!
If f:R^2->R^3 and g:R^3->R and h = g◦f, h(uv)=g(f(u,v)) for every (u,v) E R^2.
How do you calculate derivative h/u in point (a,b)?

mathmate · Answer

$$Given:\ f: R^2 \rightarrow R^3\ and \  g:R^3 \rightarrow R$$and
$$h = g◦f,\  h(u,v)=g(f(u,v))\  \forall (u,v)\in R^2$$( please confirm correction of typo in question from "h(uv)" to "h(u,v)" )

Assuming f, g and h are continuous over R, then we can use the chain rule to find the derivative of h:
$$\frac{dh}{du} = \frac{dg}{df}\frac{df}{du}$$
and evaluate the derivative at (a,b).

anonymous · Answer

yes, i made a mistake of typo.

so this mean in point (a,b) should be:

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