Question

For the equation given below, evaluate (dy/dx) at the point (1, 8/17).

(y / (x - 2y)) = x³ + 7
(dy/dx) at (1, 8/17) =

Answer 1

The student requested the calculation of the derivative (dy/dx) at a specific point on a curve represented by an implicit equation. This involves using implicit differentiation and substituting the point's coordinates into the resulting derivative to find the slope at that point.

Step-by-step explanation:

The student asked to evaluate (dy/dx) at the point (1, 8/17) for a given implicit equation. The process involves differentiating both sides of the equation with respect to x, adopting the implicit differentiation technique, and then solving for (dy/dx). Once the derivative is found, the given point values can be substituted into the derivative to find the specific slope at that point.