Question

Implicit differentiation of tan(x-y)=y/8 x²

Answer 1

To find the implicit derivative of the equation tan(x-y) = y/8 x², use the chain rule and the derivative of tangent function.

Step-by-step explanation:

To find the implicit derivative of the equation tan(x-y) = y/8 x², we will use the chain rule and the derivative of tangent function.

1. Start by differentiating both sides of the equation with respect to x.
2. Apply the chain rule to the left side by differentiating tan(x-y) as sec²(x-y)(1-dy/dx).
3. For the right side, use the power rule to differentiate y/8 x² as (1/8)(2x)(dy/dx) + (y/8)(2).
4. Simplify and solve for dy/dx, which represents the derivative of y with respect to x.

Therefore, the implicit derivative of the equation tan(x-y) = y/8 x² is dy/dx = (sec²(x-y) - y/4)/(x/4 - y/4 x²).