Find dy/dx

y = 5/8x^3/7 + 8x^4 + 6x - 9

15/56x^ (-4/7) + 32x^3 + 6.

Step-by-step explanation:

Using the rule for algebraic differentiation:

If y = ax^n, dy/dx = anx^ (n-1).

So:

If y = 5/8x^3/7 + 8x^4 + 6x - 9

dy/dx = 5/8 * 3/7 x^ (3/7-1) + 8*4 x^ (4-1) + 6x (1-1)

= 15/56x^ (-4/7) + 32x^3 + 6.