Differentiation help (Calculus)

Differentiate the following functions:

y = 8+sinx/8x+cosx

y = cosx/x^8

Rewrite cos(x)/x^8 as cos(x)*x^(-8)

Now, when you take dy/dx you can just use the product rule.

--> dy/dx = -sin(x)*x^(-8) + (-8)cos(x)*x^(-9)
=> dy/dx = -sin(x)*x^(-8) - 8cos(x)*x^(-9)

or

=> dy/dx = -sin(x)/x^8 - 8cos(x)/x^9

Whichever you prefer.

y = 8+sinx/8x+cosx
dy/dx= y1 = (8x+cosx) d(8+sinx)/dx - (8+sinx)d(8x+cosx)/dx (quotient rule)
----------------------------------------…
(8x+cosx)^2
= (8x+cosx) [cosx] - (8+sinx) [8-sinx]
----------------------------------------…
(8x+cosx)^2
y = cosx/x^8
y1= (x^8) d(cosx)/dx - (cosx) d(x^8)/dx
----------------------------------------… (quotient rule)
(x^8)^2
= (x^8) [-sinx] - (cosx) [8(x^7)]
----------------------------------------…
x^16
simplify according to reference