d/dx(csc u) = - csc u * cot u * du/dx
Your y is that
y = sqrt(x)* [csc(x+1)]^3 --> csc cubed
or
y = sqrt(x)* [csc(x+1)^3] --> x+1 cubed ?
Yes, that would be the product rule.
But then for v' you need to use the Chain Rule.
I am still not sure if the CSC function is cubed or the x+1 since it would be a difference.
v = [csc(x+1)]^3
v' = 3*[csc(x+1)]^2 * -csc(x+1)*cot(x+1) * 1
v = csc((x+1)^3)
v' = -csc(x+1)*cot(x+1) * 3*(x+1)^2 * 1
^2 means squared
^3 means cubed
Sorry, I do not know yet, how to write the functions better.
Note
Yes, but you have CSC[(x+1)^3] and not CSC(x), so for your v' you need to use the entire term in [ ]
The x in your case is (x+1)^3
Example:
f= csc(x+1)
f'= -csc(x+1)cot(x+1)
f= csc[(x+1)^3]
f'= -csc[(x+1)^3]cot[(x+1)^3]
"Hows this look?
I took the derivative of seperately from Was I supposed to do this?"
So yes but fom csc[(x+1)^3]
You always have inner and outer function
Example
f= (2-x)^3
outer function ()^3
inner function (2-x)
So,
f'= 3*(2-x)^2 * (0-1)
Hope that helps