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Chain Rule - Multivariable - Quiz, Exercises of Calculus

University of AllahabadCalculus

Main points of this past exam are: Chain Rule, Obtain Formulas, Terms, Calculate, Derivative, Use, Full Credit

Typology: Exercises

2012/2013

Uploaded on 03/21/2013

sahni
sahni 🇮🇳

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bg1
Name:
Math 206: Fall 2011
Quiz 4: November 2
For full credit you must show your work. Remember to use correct vector notation. Good Luck!
1. Let u=xln(xy) + 3y
x4;x=s+t, y =s2+st. Use the chain rule to obtain formulas for ∂u/∂ s and
∂u/∂ t. Your answers should be in terms of sand t.
1
pf2

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Name:

Math 206: Fall 2011

Quiz 4: November 2

For full credit you must show your work. Remember to use correct vector notation. Good Luck!

  1. Let u = x ln(xy) +

3 y

x

4

; x = s + t, y = s

2

  • st. Use the chain rule to obtain formulas for ∂u/∂s and

∂u/∂t. Your answers should be in terms of s and t.

  1. Let ~g(x, y, z) = (x

2

y, 3 x − xy

2

z), f (x, y) = (x/y, x + y), and ~a = (1, − 1 , 2).

(a) Calculate

Dg(~a).

(b) Use the chain rule to find the derivative of f ◦ g at ~a.