Question

given y=csc^2 x. what is the instantaneous rate of change at x = pie/2

Answer 1

first find dy/dx or y'

Answer 2

-cscx*cotx?

Answer 3

close, that's the derivative of just csc(x)

Answer 4

but you want the derivative of csc^2(x)

Answer 5

i don't know how to do that

Answer 6

use the chain rule

Answer 7

y=csc^2 x

dy/dx=2*csc x*d/dx[csc(x)]

dy/dx=2*csc x*(-csc(x)*cot(x))

dy/dx = -2*csc^2 x*cot(x)

Answer 8

now plug in x = pi/2 to find the instantaneous rate of change at x = pi/2

Answer 9

is that it?

Answer 10

yes, well you need to plug in x = pi/2 to get a value, but pretty much