Question

Find the dy/dx using implicit differentiation
for the equation below!
Thank you.
$x - 4y = e^{2x + 3y - 1}$

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Answer 1

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)