Question

Socorroooooooooooooooooooooo

Answer 1

$\dfrac{1}{cos(x^2 + 3 \cdot x +7 )} = \dfrac{\dfrac{d[1]}{dx} - \dfrac{d[cos(x^2 + 3 \cdot x +7)]}{dx} \cdot 1}{cos^2(x^2 + 3 \cdot x +7)}$

Enquanto:

$\dfrac{d[cos(x^2 + 3 \cdot x +7)]}{dx} = -sen(x^2 + 3 \cdot x + 7) \cdot (2 \cdot x + 3)$

Assim:

$\dfrac{1}{cos(x^2 + 3 \cdot x +7 )} = \dfrac{0 - [-sen(x^2 + 3 \cdot x + 7) \cdot (2 \cdot x + 3)]}{cos^2(x^2 + 3 \cdot x +7)}$

$\dfrac{1}{cos(x^2 + 3 \cdot x +7 )} = \dfrac{sen(x^2 + 3 \cdot x + 7) \cdot (2 \cdot x + 3)}{cos^2(x^2 + 3 \cdot x +7)}$

E sabendo que:

$\dfrac{sen(x)}{cos(x)} = tan(x)$,

teremos:

$\boxed{\dfrac{1}{cos(x^2 + 3 \cdot x +7 )} = \dfrac{tan(x^2 + 3 \cdot x + 7) \cdot (2 \cdot x + 3)}{cos(x^2 + 3 \cdot x +7)}}$

Alternativa D