Question

Qual a derivada de f(x) = cossec(x)³

Answer 1

Resposta:

-3.cotg(x).cossec^3(x)

Explicação passo-a-passo:

y= cossec^3(x)

y= 1/sen^3(x)

y= sen^(-3)(x)

Logo:

y'= (-3). sen^(-3-1)(x). cos(x)

y'= (-3). sen^(-4)(x). cos(x)

y'= -3.cos(x) / sen^4(x)

y'= -3.cos(x)/sen(x). 1/sen^3(x)

y'= -3.cotg(x).cossec^3(x)

Blz?

Abs :)

Answer 2

$f(x) = csc^3x\\f(x)=\frac{1}{sen^3x}\\\\f'(x)=\frac{0.sen^3x-1.(sen^3x)'}{(sen^3x)^2}\\f'(x)=\frac{-1.( 3.sen^2x.cosx)}{sen^6x}\\f'(x)=\frac{-3.sen^2x.cosx}{sen^6x}\\f'(x)=\frac{-3.cosx}{sen^4x}\\f'(x)=\frac{-3.cotgx}{sen^3x}\\f'(x)=-3.cotgx.csc^3x$

 Lembrando que:

$f(x)=senx\\f'(x)=cosx\\\\f(x)=\frac{g(x)}{h(x)}\\f'(x)=\frac{g'(x).h(x)-g(x).g'(x)}{[h(x)]^2}$

Dúvidas só perguntar!