Final answer:
To differentiate the function y = √[5]{6x}, we apply the power rule for derivatives, re-expressing the function with a fractional exponent, and then taking its derivative with respect to x. Simplifying the expression, we get ·/dx = (6/5)(6x)^(-4/5), which represents the rate at which y changes with respect to x.
Step-by-step explanation:
To differentiate the function y = √[5]{6x}, we need to apply the power rule for differentiation.
The given function can be rewritten using fractional exponents as y = (6x)^(1/5).
Using the power rule, the derivative of y with respect to x (·/dx) is then found to be (1/5)(6x)^(-4/5)·(6).
Simplifying the expression, we get ·/dx = (6/5)(6x)^(-4/5), which represents the rate at which y changes with respect to x.