Question Detail
Question
Find
dy/dx if y = cos(5x-3y).
Correct Answer
Option B is the correct answer.
Detailed Explanation
To find
dy/dx for y = cos(5x-3y), we use implicit differentiation and the chain rule:- Differentiate both sides with respect to
x:dy/dx = -sin(5x-3y) * d/dx(5x-3y) - Apply the chain rule to
d/dx(5x-3y):d/dx(5x-3y) = 5 - 3 dy/dx - Substitute this back into the equation:
dy/dx = -sin(5x-3y) * (5 - 3 dy/dx)dy/dx = -5sin(5x-3y) + 3sin(5x-3y) dy/dx - Rearrange the terms to group
dy/dxon one side:dy/dx - 3sin(5x-3y) dy/dx = -5sin(5x-3y)dy/dx (1 - 3sin(5x-3y)) = -5sin(5x-3y) - Solve for
dy/dx:dy/dx = -5sin(5x-3y) / (1 - 3sin(5x-3y))
Hint
Remember to use implicit differentiation and the chain rule. Gather all
dy/dx terms on one side.