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Assume that z=f(w),w=g(x,y),x=4r3−s2, and y=rs. If gx​(4,1)=−3,gy​(4,1)=4,f′(8)=−3, and g(4,1)=8, find the following. ∂r∂z​∣∣​r=1,s=0​ and ∂s∂z​∣∣​r=1,s=0​ Calculate ∂r∂z​∣∣​r=1,s=0​ and ∂s∂z​∣∣​r=1,s=0​ ∂r∂z​∣∣​r=1,s=0​=□∂s∂z​∣∣​r=1,s=0​=□​
Find ∂u∂z​ when u=−1,v=0, if z=sin(xy)+xsin(y),x=u2+3v2, and y=3uv. ∂u∂z​∣∣​u=−1,v=0​= (Simplify your answer.)