Show all work and include appropriate explanations when space is provided. Instructions. answers unaccompanied by work may not receive full credit. The last page contains some useful identities: (10 pts) find the indicated derivatives. No need to simplify. (a) (5pts) dx(ex3+x) (b) (5pts) dx(ln 3 x: (10pts) find the indicated antiderivatives. 5x + 2 dx (b) (5pts) z x2 sin (x3) dx: (6pts) use logarithmic di erentiation to nd the derivative of y = 1 + x x7/5 (a) (3pts) first, take the natural logarithm of the both sides and simplify using the properties of log. (b) (3pts) next, di erentiate both sides with respect to x and solve for dy dx . Hint: conclude something from f (x). (b) (2pts) fill in the blank: f 1(3) = (c) (3pts) compute (f 1) (3), i. e. compute the derivative of the inverse function to f evaluated at 3: (10pts) evaluate the following.
