Explanation

You gave the equation:  

xy² + xy = 8x  

We are to find dy/dx at the point (1, 2).

---

Step 1: Differentiate both sides implicitly with respect to x:

d/dx(xy²) + d/dx(xy) = d/dx(8x)

Use product rule:  

d/dx(xy²) = x·d/dx(y²) + y²·d/dx(x) = x·2y·dy/dx + y²  

d/dx(xy) = x·dy/dx + y  

d/dx(8x) = 8

So the full derivative becomes:  

x·2y·dy/dx + y² + x·dy/dx + y = 8

Now plug in x = 1, y = 2:

1·2·2·dy/dx + 4 + 1·dy/dx + 2 = 8  

=> 4·dy/dx + 4 + dy/dx + 2 = 8  

=> 5·dy/dx + 6 = 8  

=> 5·dy/dx = 2  

=> dy/dx = 2/5