Sunday, 18 August 2013

Exercise concerning the definition of the partial derivative

Exercise concerning the definition of the partial derivative

I found this practice problem for an exam, and I haven't been able to make
a satisfactory answer. It goes like this:
Let $g(t)=f(t^2+1,t)$, where $f(x,y)$ is a differentiable function. If
$f_y(1,0)=0$, then $g'(0)=0$. Is this true or false?
Because it is a practice problem, I checked the answer and it said it was
true. I've tried using the fact that if $f_y(a,b)$ exists, that implies
that there is a function $G$ such that $G'(b)=f_y(a,b)$ where
$G(y)=f(a,y)$. But the $g$ that I was given is a function of $t$, so there
can not be a constant parameter for $f$.
I'm completely clueless, and getting more confused the more I think. Any
help would be appreciated.
EDIT: There actually was a typo. The function was $g(t)=f(t^2+1,t)$

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