Calculus  Differentiation  Implicit Differentiation.
Test Yourself 1.
Direct differentiation.  Use implicit differentiation to find

Derive the equation of the following hyperbola  
Find the derivative of y^{2} = x^{2}y + 1.


Stationary points.  Find the coordinates of any stationary points for the curve
y^{3} + 2xy + x^{2} + 2 = 0.

Find the coordinates of the points where the tangent to the curve x^{2} + 2xy + 3y^{2} = 8 is horizontal.


Gradients.  Find the equation of the tangent to the curve defined by
x^{2}  xy + y^{3} = 5 at the point (2, 1).

Find the coordinates of the point where the tangent to the curve x^{2}  y^{2} + xy + 5 = 0 is parallel to the line y = x.


A plane curve is defined implicitly by the equation
x^{2} + 2xy + y^{5} = 4. This curve has a horizontal tangent at P (x, y). Show that x is a root of the equation x^{5} + x^{2} + 4 = 0. 