#1 If a and b are lengths of two sides of a triangle, and theta the measure of hte included angle, the area A of hte triangle is A = (1/2)absin(theta). How is dA/dt related to da/dt, db/dt, and dtheta/dt?

My work:

A= (1/2)absin(theta)

dA/dt = ((1/2)(ab))'sin(theta) + (1/2)ab(sin(theta))'

dA/dt = ((1/2)(dA/dt)b + (1/2)a(db/dt))sin(theta) + (1/2)abcos(theta)(theta)'

I think there's something wrong either in the power rule or the (theta)'.

#2 Why do we use the formula

D^2 = x^2 + y^2 in the following question?...

A point moves smoothly along the curve y = x^(3/2) in the first quadrant in such a way that its distance from the origin increases at the constant rate of 11 units per second. Find dx/dt when x = 3.

I know the answer is dx/dt = 4 units per second. I just want to know why we use that formula, and other potential scenerios of when we might use it.