Qual é a derivada de cosec x?

#"differentiate using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#"here "y=cscx=1/sinx=(sinx)^-1#

#rArrdy/dx=-(sinx)^-2xxd/dx(sinx)#

#color(white)(rArrdy/dx)=-cosx/(sin^2x)#

#color(white)(rArrdy/dx)=-cosx/sinx xx1/sinx#

#color(white)(rArrdy/dx)=-cotxcscx#