Given y = x(3x+ 5)^3. Find dy/dx.

First we notice that y can be written as the product of two functions of x, u = x and v = (3x + 5)^3. This means we can use the product rule to differentiate which is dy/dx = uv' + vu'. We can plug our functions u and v into this formula, using the chain rule to differentiate v to arrive at dy/dx = (3x + 5)^3 + 9x(3x + 5)^2. Next we need to simplify by taking out a common factor to get (3x + 5)^2 ((3x +5) + 9x)). Which we can further simplify to (3x + 5)^2 (12x + 5) which is the final answer.