I missed my class on this and dont know how to solve

Question

We can write y=sin(u) where

u=___

The notation for the chain rule is

dy/dx=dy/du*du/dx

The factors are

dy/du=___(written as a function of u ) and

du/dx=___(written as a function of x).

Now substitute in the function of x for u to get

dy/dx=___(written as a function of x).

Answer 1

Here is a Desmos graph that shows how you can use Desmos to verify a calculated derivative:

desmos.com/calculator/g1kwfjmims

Answer 2

y = sin(6x -2x⁵- 2)

they ask you to try writing y = sin(u), therefore

u = 6x - 2x⁵ -2

dy/du = cos(u)

du/dx = 6 - 10x

chain rule says: dy/dx = dy/du * du/dx, plug in terms from above

dy/dx = cos(u) * (6-10x)

replace u

dy/dx -= cos(6x - 2x⁵ -2)*(6 - 10x)