Question

(1) Derive as seguintes funções:

c) y = $\sqrt{sin \ 6 x}$
d) k(x) = sin (x²+2)

Answer 1

Resposta:

Explicação passo-a-passo:

Olá,

c)

Observe que:

$y=\sqrt{sin 6x} => y=(sin 6x)^{\frac{1}{2}}$

Logo:

$y' = \frac{1}{2} (sin\ 6x)^{\frac{-1}{2}} 6\ cos\ 6x \\\y' = \frac{3x\ cos\ 6x}{(sin\ 6x)^{\frac{1}{2}}}\\\y' = \frac{3x\ cos\ 6x}{\sqrt{sin\ 6x} }$

d)

$k(x) = sin (x^2 +2)\\\k'(x) = cos (x^2 + 2)\ 2x\\\k'(x) = 2x cos (x^2 +2)$