Question

the slope of the curve y^4=y^2-x^2
at the point (sqrt(3)/4 , 1/2)

Answer 1

Differentiate implicitly then evaluate at x = sqrt(3/4) and y = 1/2

Answer 2

\[4y^3 y' = 2y y' + 2x\]
\[y' = \frac{2x}{4y^3 - 2y}\]
plug in point
\[y' = \sqrt{3}\]