The curve C is defined by x^3 – (4x^2 )y = 2y^3 – 3x – 2. Find the value of dy/dx at the point (3, 1).

When we find dy/dx we find the gradient of the curve at (3,1). Start by differentiating the left hand side (LHS) like so.. (whiteboard). Remember every time we differentiate a y value we multiply by dy/dx. This is because we differentiate y with respect to y and then multiply by dy/dx to get y differentiated with respect to x (by the chain rule). We now differentiate the RHS... (whiteboard) Now collect the dy/dx terms on the LHS and the other terms on the RHS like so... (whiteboard) Now sub in x=3 and y=1 and we obtain dy/dx=1/7.