TeX source:
\begin{array}{rcl}f'_x(x,y) &=& 4\cos(x)-\sin\left(-\dfrac{1}{4}x+y\right)\cdot\left(-\dfrac{1}{4}\right)\\&=& 4\cos(x)+\dfrac{1}{4}\sin\left(-\dfrac{1}{4}x+y\right)\end{array}