I might have to keep coming back here, this assignment is killing me...

Given w = xy + yz, y = sin x and z = e^x, find dw/dx

But if you sub in the values for y and z before taking the derivative, you get:

Different from the top answer. Can anyone see where I went wrong?

Also:

Given u = x + ay and v = x + by, for what values a and b can you change:

to:

At first I tried to factor it into (3n - 2m)(3n - m), but then I remembered that the second derivative doesn't equal the first derivative squared. Also, the middle term isn't necessarily both partial derivatives multiplied together. I found:

and:

But I can't think of a way to sub them in, or take the next derivative without knowing what f is.