Fevereiro 19, 2020

por Ree

Qual é a derivada de ${cos x}^{3}$ $cosx ^ 3$ ?

Responda:

$- 3 x^{2} {sin x}^{3}$ $-3x^2sinx^3$

Explicação:

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

$color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x)).g'(x))color(white)(a/a)|))....(A)$

$f(g(x))=cos(x^3)rArrf'(g(x))=-sin(x^3)$

and $g(x)=x^3rArrg'(x)=3x^2$
$"----------------------------------------------------"$
Substitute these values in $color(red)"(A)"$

$rArrd/dx(cosx^3)=-sinx^3 .3x^2=-3x^2sinx^3$