Question

dy/dx of y+1/2=sin(x-y)+pie/3

Answer 1

\[\frac{d}{dx}(y+\frac{1}{2})=\frac{d}{dx}(\sin(x-y)+ \frac{\pi}{3})\]

Answer 2

Distribute:
\[\frac{d}{dx}(y)+\frac{d}{dx}(\frac{1}{2})=\frac{d}{dx}(\sin(x-y))+\frac{d}{dx}(\frac{\pi}{3})\]

Answer 3

Recall derivative of a constant is 0 and also recall derivative of y with respect to x is dy/dx.

Now are you having touble with the dsin(x-y)/dx part?

Answer 4

\[\text{ hint: } \frac{d}{dx}(\sin(x-y))= \text{ (By chain rule) } \frac{d}{dx}(x-y) \cdot (\frac{d}{dx} \sin) (x-y)\]
Derivative of inside function times the derivative of the outside function (when taking derivative of outside make sure leave inside the same)