TeX source:
\begin{array}{rcl} f'_y(x,y,z) &=& \dfrac{\pi x\cos\left(7y^5\right)\cdot 35y^4}{e^{10xz+1}} \cr \cr &=& \dfrac{35\pi xy^4\cos\left(7y^5\right)}{e^{10xz+1}} \cr\cr&=& 35\pi xy^4\cos\left(7y^5\right)e^{-10xz-1}\end{array}