Appropriate Chain Rule

Most students think of mathematics study as a sequence of calculations involving the use of predetermined quantities and formulae that need to be remembered. This gives people the impression that mathematics is difficult to understand. The authors at My Homework Writers are the best. One illustration of such a query is;

1) Consider the following.  w = yz/x, x = θ2, y = r + 7θ, z = r − 7θ

(a) Find ∂w/∂r and ∂w/∂θ by using the appropriate Chain Rule.  ∂w∂r  =  ∂w∂θ=

(b) Find ∂w/∂r and ∂w/∂θ by converting w to a function of r and θ before differentiating.  ∂w∂r=∂w∂θ=

2) Evaluate fx, fy and fz at the given point.  f(x, y, z) = x2y3 + 7xyz − 5yz, (−1, 2, 1)  fx(−1, 2, 1)  =  fy(−1, 2, 1)=

3) For f(x, y), find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously.  f(x, y) = x2 + 4xy + y2 − 18x − 12y + 14  (x, y) =

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