Qual é a derivada de cosec x?

Responda:

$- cot x csc x$ $-cotxcscx$

Explicação:

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

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

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

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

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

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

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

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