You must show all work to receive full credit. The following formulae may be used: (a > 0) A2 x2 a2 + x2 = dx. = arcsin(cid:18) x arctan(cid:18) x a(cid:19) + c a(cid:19) + c arcsec |x| a ! X2 a2 a2 x2 = x a2 x2 dx. = ln(x + x2 a2) + c ln(cid:12)(cid:12)(cid:12)(cid:12) a x(cid:12)(cid:12)(cid:12)(cid:12) ln a + a2 x2. + c: find the derivatives of the following functions. [8 points] a). y = ln x + 1 x 1! Find the derivative of y = xx using logarithmic di erentiation. [2 points] b) find the tangent line to y = xx at the point x = 1. Implicitly di erentiate the following equation with respect to x and solve for y . exy + x2 + y2 = 1. Find where the function f (x) = e x. 2 is increasing and where it is decreasing: evaluate the following integrals.
