Question

Use implicit differentiation to obtain dy over dx

Cosx +sinx=xsquared+ysquared

Answer 1

Ans:-

$Cosx +Sinx=x^2+y^2\\$ then $y=\sqrt{Cosx+Sinx-x^2}$

Differentiate both side with respect to x

$\Rightarrow -Sinx+Cosx=2x+2y\dfrac{dy}{dx}\\ \Rightarrow \dfrac{dy}{dx}=\dfrac{Cosx-Sinx}{2x+2y}\\$

$\Rightarrow \dfrac{dy}{dx}=\dfrac{Cosx-Sinx}{2(x+\sqrt{Cosx+Sinx-x^2})}$