Differential Calculus

Find the volume of the largest right circular cylinder that can be cut from a circular cone of radius 6cm and height 9cm?

Find the differential equation of parabolas with vertex and focus on the x-axis.

Here's my question:
Example: examine the function
Y=x(x-1)^3
Y'=3x(x-1)^2+(x-1)^3=(x-1^2(4x-1)
Y"=4(x-1)^2+2(x-1)(4x-1) ... How did they get 4(x-1)^2+2(x-1)(4x-1)?

Hi! I need help with these.

Please Help. (1+e^(x) y+x e^(x) y) dx + (x e^(x) + 2)dy=0

Please help. Been staring at it for a few hours now.

cosysin2xdx +(cos^2y - cos^2x)dy = 0

https://ibb.co/g9Vk3b

https://ibb.co/fZh4ww

How do I solve these? Help po.

Help me find the limits of these:

https://imgur.com/a/yobgF

Help me identify all asymptotes and the end behavior of the graph:

https://imgur.com/a/JxJF2

Guys may complete solution ba kayo sa mga problems sa DE..?