Question

Find the second derivative of x^2-y^2=1

Answer 1

Have you covered implicit differentiation? If so, here goes:

d/dx(x^2 +y^2 = 1) = 2x + 2ydy/dx = 0, so dy/dx = -x/y.

Differentiating dy/dx gives (using the quotient rule) gives d^2y/dx^2 = ( -y +xdy/dx)/y^2

Substituting for dy/dx gives the second differential -(x^2 + y^2)/y^3