Final answer:
To evaluate (dy)/(dx) for the equation x⁴/⁵+y⁴/⁵=82 at the given point (243,1), differentiate the equation with respect to x using the Power Rule of Differentiation and substitute the given values.
Step-by-step explanation:
To evaluate (dy)/(dx) for the equation x⁴/⁵+y⁴/⁵=82 at the point (243,1), we need to find the derivative of y with respect to x and substitute the given values.
First, let's differentiate x⁴/⁵+y⁴/⁵=82 with respect to x using the Power Rule of Differentiation. The derivative of x⁴/⁵ with respect to x is (4/5)x^(-1/5), and the derivative of y⁴/⁵ is (4/5)y^(-1/5).
Substituting the given values x=243 and y=1 into the derivatives, we get (dy)/(dx) = (4/5)(243)^(-1/5) + (4/5)(1)^(-1/5).