Question

hi how to solve derivative with respect to x when the actual function is f(x)= sinx+y^2+cosy what manupilations will be performed on variable y when we will solve this eq with respect to x

Answer 1

\[\frac{\delta}{\delta x} \sin x + y^2 + \cos y=\frac{d}{dx} \sin x + \frac{d}{dx} y^2+ \frac{d}{dx} \cos y\]
\[=\cos x + 0 + 0 = \cos x\]

Answer 2

In addition to what agreene posted, the manipulation performed on y is just holding it constant.