y = 4x^(3/4) + 3x^(2/3) + 4x^(1/2) + 3x

The derivative of the first function is:

1. Differentiate each term using the power rule: d/dx(ax^n) = anx^(n-1).
2. Apply the rule to each term: 4*(3/4)x^(-1/4) + 3*(2/3)x^(-1/3) + 4*(1/2)x^(-1/2) + 3.
3. Simplify the expression: 3x^(-1/4) + 2x^(-1/3) + 2x^(-1/2) + 3.

Result: 3x^(-1/4) + 2x^(-1/3) + 2x^(-1/2) + 3