Final answer:
The slope of the curve x⁴⁄⁵+y⁴⁄⁵=2 at the point (1,1) is found by differentiating the equation implicitly and evaluating the resulting derivative dy/dx at the specific point.
Step-by-step explanation:
To determine the slope of the curve x⁴⁄⁵+y⁴⁄⁵=2 at the point (1,1), we need to find the slope of the tangent line at that point. This involves differentiating the given equation with respect to x, implicitly, since the equation is not solved for y. Let's go through the steps to find the derivative and subsequently the slope at the specified point:
- Differentiate both sides of the equation with respect to x. This involves using the power rule and chain rule for differentiation.
- After differentiating, solve for the derivative dy/dx to find the slope of the tangent line.
- Evaluate dy/dx at the given point (1,1) to find the specific slope at that point.