Solve the below:
Q1: a) Find the derivative of the following functions dy/dx, by the method of implicit differentiation: i) (x^2)(y^2) - xy = 8; ii) sqrt(x + y) = x; iii) (x - y)/(2x + 3y) = 2x.
b) Find the equation of tangent line to the graph of the following function at the indicated points: i) y^2 - x^2 = 16; at (2, 2 sqrt(5); ii) (x^2)(y^3) - y^2 + xy - 1 = 0 at (1, 1).
Q2: a) Find the derivative of the following functions: i) f(x) = 4e^(3x+2) ... ii) f(x) = (x^3)(e^x); iii) f(x) = (x-1)e^3x+2; iv_ Find the second derivative of the function: f(x) = 2xe^3x.
b) i) find an equation of the tangent line to the graph of the function f(x) = xln, at; (1,1). ii) Find the equation of the tangent line to the graph of y = e^2x-3 at (3/2, 1).