Question

use quotient rule to show d/dx(cscx)=-cscxcotx

Answer 1

hi do you know whats identity of 1/cscx?

Answer 2

no

Answer 3

csc x=1/sin x do the derivative of this using the quotient rule
d(csc x)dx=d(1/sin x)dx=?

Answer 4

quotient rule says d(u/v)dx=(v du/dx - u dv/dx)/v^2

Answer 5

u+1 and v=sin x
\[d(\frac{ 1 }{ \sin x })/dx=\frac{ \sin x(d(1)/dx)- 1 d(\sin x/dx)}{ (\sin x)^2 }\]
=\[\frac{ -\cos x }{ (\sin x)^2 }=\frac{ 1 }{ \sin x }*\frac{ \cos x }{ \sin x }=-\csc x \cot x\]

Answer 6

that was u=1 and v=sin x