Find the second derivate d^2y/dx^2 when y = x^6 + sqrt(x).

Initially we find the first derivative of the function y = x⁶ + sqrt(x). We achieve this by multiplying each x term by the power it is raised to, then reducing the power by 1. Solution:
1) It helps to initially simplify the sqrt(x) term to x^1/2 to give: y = x⁶ + x^1/2
2) We can then determine the first derivative: dy/dx = 6x⁵+ 1/2x^-1/2
To determine the second derivative we then take the first derivative and differentiate that function, repeating the prior steps:
3) d²y/dx² = 30x⁴ + (-1/4)x^-3/2
We can simplify the answer to give:
4) d²y/dx² = 30x⁴ -1/4x^-3/2
Simplifying fully gives:
5) d²y/dx² = 30x⁴ - (1/(4x^3/2))