Find the differential of each function.(a)    y = s/(2 + 9s)dy = (b)    y = u cos udy =

(a) To find the differential of the function y = s/(2 + 9s), we will use the quotient rule for differentiation which states that the derivative of two functions f and g, f/g, is (gf' - fg')/g^2.

Let's denote: f(s) = s and g(s) = 2 + 9s

The derivatives of f and g are: f'(s) = 1 and g'(s) = 9

Using the quotient rule, the derivative of y with respect to s is:

dy/ds = (g(s)*f'(s) - f(s)*g'(s))/g(s)^2 = ((2 + 9s)1 - s9)/(2 + 9s)^2 = (2 + 9s - 9s)/(2 + 9s)^2 = 2/(2 + 9s)^2

(b) To find the differential of the function y = u cos u, we will use the product rule for differentiation which states that the derivative of two functions f and g, f*g, is f'g + fg'.

Let's denote: f(u) = u and g(u) = cos u

The derivatives of f and g are: f'(u) = 1 and g'(u) = -sin u

Using the product rule, the derivative of y with respect to u is:

dy/du = f'(u)g(u) + f(u)g'(u) = 1cos u + u(-sin u) = cos u - u sin u