Can you help me with those please.

1. Suppose that f and g are differentiable functions and let h(x) = f (x)g(x)

(a) Show that h = f g1 (f g + f gln f )

(b) If f (x) = b (where b is a strictly positive constant), show that the formula in part (a) simplifies into a formula we have seen earlier in this course.

(c) If g(x) = n (where n is a constant), show that the formula in part (a) simplifies into a familiar formula we have seen earlier in this course

2. An ordinary differential equation (ODE) is an equation that contains an unknown function y(x) and some of it's derivatives y(x), y(x), etc. Many of you will take a course in your second year that will show you how to solve ODEs. Solving an ODE means finding a function y(x) that satisfies the equation. In this question, we've done the solving for you! You will be showing that a given function is a solution to an ODE. Consider the following ordinary differential equation y(x) + y(x) 2y(x) = 4x2

(a) . Show that y(x) = 2x2 + 2x + 3 is a solution to the ODE given above.

(b) For what values of r is y(x) = erx + 2x2 + 2x + 3 also a solution to the ODE given above?