Answer:
dy/dx = (1 − 2x + 8y) / (4 + 3x − 12y)
Explanation:
d/dx (x − 4y) = d/dx (e^(2x + 3y − 1))
1 − 4 dy/dx = e^(2x + 3y − 1) (2 + 3 dy/dx)
Since x − 4y = e^(2x + 3y − 1):
1 − 4 dy/dx = (x − 4y) (2 + 3 dy/dx)
1 − 4 dy/dx = 2 (x − 4y) + 3 (x − 4y) dy/dx
1 − 4 dy/dx = 2x − 8y + (3x − 12y) dy/dx
1 − 2x + 8y = (4 + 3x − 12y) dy/dx
dy/dx = (1 − 2x + 8y) / (4 + 3x − 12y)
