Find the derivative of:
Tbh the Csc is throwing me off here. I'm unsure what to apply here. I know that the chain rule and product rule will be used but I'm stuck.
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