Answer
Undefined
Work Step by Step
$y^2=\frac{x^2-49}{x^2+49}$
$y^2(x^2+49)=x^2-49$
$x^2y^2+49y^2=x^2-49$
$\frac{d}{dx}[x^2y^2+49y^2]=\frac{d}{dx}[x^2-49]$
$2xy^2+2x^2y\frac{dy}{dx}+98y\frac{dy}{dx}=2x$
$2xy^2+(2x^2y+98y)\frac{dy}{dx}=2x$
$(2x^2y+98y)\frac{dy}{dx}=2x-2xy^2$
$\frac{dy}{dx}=\frac{2x-2xy^2}{2x^2y+98y}$
$\frac{dy}{dx}=\frac{x-xy^2}{x^2y+49y}$
$(7,0)$
$\frac{x-xy^2}{x^2y+49y}=\frac{(7)-(7)(0)^2}{(7)^2(0)+49(0)}=\frac{7}{0}$
Undefined.
