1. Differentiate the following with respect to x: a) In C 4x+3. 2x-5 [4] b) 3* Inx [5] c) Vx2 + 1 [4] d) e z [3] 2. Given that y = (a + bx)e- where a and b are constants, show that dx2 + 2- arty = 0 [8] 3. Find for 7x3 + 4y = 3y2 [4] dx 4. Given the equation 2y2 - 2xy - 4y + x2 = 0 of a curve, obtain the x-coordinates of each point at which the curve has a horizontal tangent. [6] 5. Find the gradient of cos(xy) - 3y4 + 3 at the point (1, ") [5] 6. Find the equation of the tangent to the curve xy + y3 = 6x + 3y at (1,2) [7]