What is the derivative of ?

#1/sinx -1/tanx#

2 Answers
Mar 30, 2018

# cscx(cscx-cotx)#.

Explanation:

#d/dx{1/sinx-1/tanx}#,

#=d/dx{csc x - cotx}#,

#=d/dx(cscx)-d/dx(cotx)#,

#=-cscxcotx-(-csc^2x)#,

#=cscx(cscx-cotx)#.

Mar 30, 2018

#csc^2x-cscxcotx#

Explanation:

#1/sinx-1/tanx#

#=cscx-cotx#

#"these are "color(blue)"standard derivatives"#

#d/dx(cscx)=-cscxcotx" and "d/dx(cotx)=-csc^2x#

#rArrd/dx(1/sinx-1/tanx)=-cscxcotx+csc^2x#