Question

a) Find an equation of the tangent line at the origin to the curve .

1+sin(x+y)=xy+cosy

Answer 1

tangent line:

$y-y_0=y'(x_0)(x-x_0)$

we have:

$(x_0,y_0)=(0,0)$

$y'cos(x+y)=y+xy'-y'siny$

$y'=\frac{y}{cos(x+y)+siny-x}$

$y'(0)=0$

then, equation of tangent line:

$y=0$