Problem 1 (4 points). Using the definition of the derivative, f'(x) = lim /(ath) - f(x) h-+ h show that if f(x) = =, where a is the last digit of your student number, then f'(x) = -- Note: If the last digit of your student number is 0 or 1, use the last one that is not 0 or 1 instead. Problem 2 (4 points). Compute the first four derivatives of g(x) = sin(x) - 73. Problem 3. Let h(x) = In(x) + x2. . Find the tangent line of h(x) at a = 1. (2 points) . Using this tangent line, approximate h(1.01). (2 points) Using implicit differentiation, find the derivatives given the following equations: . xy = 1: dy/dx = -y/x . xly? = 1: dy/dx = -y/x . sin(xy) = 1: dy/dx = -y/x . In(xy) = 1: dy/dx = -y/x 7 Let f(t) = (3t - 5)5. Then the equation of tangent line at t = 2 is y = out of Let f(t) = 5cus(2). For the chain rule, the "inside function" is g() = and so g' (t) = * . The derivative of the "outside function" is h'(t) = Therefore f'(t) - h'(g(0))g'(t)