Final answer:
To find dy/dx, we can use the chain rule for differentiation. The derivative of y = u^(1/3) is (1/3) * u^(-2/3). The derivative of u = x^5 is du/dx = 5x^4.
Step-by-step explanation:
To find dy/dx, we can use the chain rule for differentiation. If we let u = x^5, then we have y = u^(1/3).
Using the chain rule, dy/dx = (dy/du) * (du/dx).
The derivative of y = u^(1/3) is dy/du = (1/3) * u^(-2/3).
The derivative of u = x^5 is du/dx = 5x^4.
Substituting these values into the chain rule equation, we have dy/dx = (1/3)*(u^(-2/3))*(5x^4).
When x = 8, we can substitute this value into the equation to find the derivative.
Therefore, dy/dx = (1/3)*(8^(5/3))^(-2/3)*(5(8^4)).