Given that y = x^4 + x^(1/3) + 3, find dy/dx

We use the rule that if y = x^n then dy/dx = n*x^(n-1) which is valid whether or not n is an integer. 

We also use that differentiation is a linear operation, which means that we can differentiate term by term in the expression for y.

Noting that 3 = 3*x^0, we therefore have

dy/dx = 4*x^3 + (1/3)*x^(-2/3) + 0