Question

if y+siny=cosx find Dy/dx​

Answer 1

Step-by-step explanation:

so the answer is -sinx/(1+cosy)

Answer 2

Question:-

If $\sf y+ \sin(y)=\cos(x)$, find $dy/dx$.

Solution:-

Given,

$\sf y + \sin(y) = \cos(x)$

Differentiating both side by x,

$\sf \frac{dy}{dx} + \frac{d( \sin(y) )}{dx} = \frac{d( \cos(x)) }{dx}$

$\sf \implies \frac{dy}{dx} + \frac{d( \sin(y) )}{dx} = - \sin(x)$(As cos(x)'= -sin(x))

$\sf \implies \frac{dy}{dx} + \frac{d( \sin(y) )}{dy} \times \frac{dy}{dx} = - \sin(x)$

$\sf \implies \frac{dy}{dx} + \cos(y)\frac{dy}{dx} = - \sin(x)$(As sin(x)'=cos x)

$\sf \implies \frac{dy}{dx}(1 + \cos(y)) = - \sin(x)$

$\sf \implies \frac{dy}{dx} = \frac{ - \sin(x) }{1 + \cos(y)}$

Hence,

$\boxed{ \sf \frac{dy}{dx} = \frac{ - \sin(x) }{1 + \cos(y)} }$