Write a chain rule formula for the following derivative. dw for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t) at dw dw dx dw dy + at dx dt dy at O dw at aw dw + dx dw dy dz O dw at dw dx dx at dw dy dw dz dy at dz at O dw at aw dy dw dx + ax dr dw dz %3D dy ds dz at + + + II II

Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y & z considering other as constant at…

Q: d y. d3y dy d'y dy (+() dy + y dt2" dt + b dt dt2 ay dt3 d/dt (5 %3D dt

A: Explained below

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(3,…

A: Directional Derivative, Du f(x,y,z) = ∇f(x,y,z).u ; where , u is the unit vector  .

Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(1,…

A:

Q: Find the derivative of f(x, y, z)=x²-xy² -z at the point p (1,1,0) in the direction of V=i-j+2k (it…

A: