anonymous
  • anonymous
dy/dx of y+1/2=sin(x-y)+pie/3
Mathematics
katieb
  • katieb
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myininaya
  • myininaya
\[\frac{d}{dx}(y+\frac{1}{2})=\frac{d}{dx}(\sin(x-y)+ \frac{\pi}{3})\]
myininaya
  • myininaya
Distribute: \[\frac{d}{dx}(y)+\frac{d}{dx}(\frac{1}{2})=\frac{d}{dx}(\sin(x-y))+\frac{d}{dx}(\frac{\pi}{3})\]
myininaya
  • myininaya
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?

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

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