Partial Derivative – A three variable function – Exercise 3279

u'_x (x,y,z)=\frac{y}{z}\cdot x^{\frac{y}{z}-1}

u'_y (x,y,z)=x^{\frac{y}{z}}\ln x\cdot\frac{1}{z}

u'_z (x,y,z)=x^{\frac{y}{z}}\ln x\cdot\frac{-1}{z^2}