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  4. If sin (x+y)+ cos (x+y)= log (x+y) then (d2 y/d x2)

Q. If $\sin (x+y)+\cos (x+y)=\log (x+y)$ then $\frac{d^{2} y}{d x^{2}}$

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Solution:

$\sin (x+y)+\cos (x+y)=\log (x+y)$
$\cos (x+y)\left(1+y_{1}\right)-\sin (x+y)\left(1+y_{1}\right)-\frac{1}{x+y}\left(1+y_{1}\right)=0$
$\therefore 1+y_{1}=0$
$\therefore y_{1}=-1$
$\therefore y_{2}=0$
$\therefore \frac{d^{2} y}{d x^{2}}=0$

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