2021-10-02

Higher-order derivatives Find and simplify y.
$x+\mathrm{sin}y=y$

Alix Ortiz

Step 1
Given: $x+\mathrm{sin}y=y$
To compute : y''
formula: ${\left(\mathrm{sin}x\right)}^{\prime }=\mathrm{cos}x$
${\left(\mathrm{cos}x\right)}^{\prime }=-\mathrm{sin}x$
Step 2
Lets differentiate the given function with respect to x
${y}^{\prime }=1+\mathrm{cos}y$
Again differentiating above y' we get
$y{}^{″}=-\mathrm{sin}y$
$⇒y{}^{″}=-\left(y-x\right)$
$⇒y{}^{″}=-y+x$

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