<s>[INST] Taking the derivative of $y = \dfrac{x}{2}  + \dfrac {1}{4} \sin(2x)$ Again a simple problem that I can't seem to get the derivative of
I have $\frac{x}{2} + \frac{1}{4}\sin(2x)$
I am getting $\frac{x^2}{4} + \frac{4\sin(2x)}{16}$
This is all very wrong, and I do not know why.
 [/INST] If $f(x) = \frac{x}{2} + \frac{1}{4}\sin(2x)$, then $f'(x) =$ $\frac{1}{2} + \frac{cos(2x)}{2}$. If you want $\int{f(x)}$, then we have $\frac{x^2}{4} - \frac{cos(2x)}{8}+C$. Here, we differentiate/integrate $\frac{x}{2}$ and  $\frac{1}{4}\sin(2x)$ separately. Do you have an initial condition?
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