1.)dy/dx for 3x^7+5/x^3+3(7square roots of x^2)+sinx

2.)d/dx sinx/6x^4

3.)d/dx sin(6x^4)

4.)d/dx sin^4(6x)

Dunno what "7square roots of x^2" are.

Moving on,
2. use the quotient rule
(uv)' = (u'v - uv')/v^2
(cosx * 6x^4 - sinx * 24x^3)/36x^8
= (x cosx - 4 sinx)/6x^5

3. Use the chain rule
dy/dx = dy/du * du/dx

cos(6x^4) * 24 x^3

3. Use the chain rule twice:

4sin^3(6x) * 6 cos(6x) = 24 sin^3(6x) cos(6x)