Question

Calcule y´ por derivação implícita a y² = x.cos y

Answer 1

$\displaystyle \sf y^2 =x\cdot cos\ y \\\\ Derivando : \\\\ 2\cdoy y\cdot y' =1\cdot cos\ y+x\cdot (-sen\ y)\cdot y' \\\\ 2y\cdot y '=cos\ y -x\cdot sen\ y \cdot y' \\\\ 2y\cdot y' +x\cdot sen \ y \cdot y' = cos \ y \\\\ y' \cdot (2y+x\cdot sen\ y )=cos\ y \\\\\\ \huge\boxed{\sf y' = \frac{cos\ y }{2y+x\cdot sen\ y }}\checkmark$

Answer 2

Resposta:

y' = cosy/(2y + xseny)

Explicação passo a passo:

y² = x.cos y

2yy' = x (-seny . y') + cosy . 1

2yy' + xsenyy' = cosy

y'( 2y + x seny) = cosy

y' = cosy/(2y + xseny)