(a) Let z(x,y)=e^3xy,x(p,q)=p/q and y(p,q)=q/p are functions. Use multivariable chain rule of partial derivatives to find (i) ∂z/∂p (ii) ∂z/∂q. (b) Find the directional derivative of the function...

(a) Let z(x,y)=e^3xy,x(p,q)=p/q and y(p,q)=q/p are functions. Use multivariable chain rule of partial derivatives to find


(i) ∂z/∂p

(ii) ∂z/∂q.

(b) Find the directional derivative of the function g(x,y ,z)= y-√(x^2+z^2 ) at the point

P(-3, 1, 4) in the direction of vector a ⃗=2i-2j-k.