Consider the curve given by $\displaystyle 2xy - \sqrt{x^2+y}=-23$.
Find the equation of the line tangent to the curve at the point (−2, 5)
Thanks
Differentiating implicitly we get $\displaystyle 2xy'+2y-\frac{1}{2}(x+2y)^{\frac{-1}{2}}\cdot(2x+y')=0$ now using this we get $\displaystyle y-5=f'(-2,5)(x+2)$ I will leave the evaluation of f'(-2,5) to you...plug it in and solve for y'