MATH200 December 2011
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 • Q5 (a) • Q5 (b) • Q6 • Q7 • Q8 (a) • Q8 (b) i • Q8 (b) ii • Q8 (b) iii •
Question 02 (a)
Suppose z = f(x,y) has continuous second order partial derivatives and x = r cos(t), y = r sin(t). Express the following partial derivatives in terms of r,t and the partial derivatives of f.
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To evaluate this partial derivative we need to use the chain rule.
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The variable z is a function of both x, y which, in turn, are both functions of t. Thus, any change in z in response to a change in t will be the result of how x and y change with t. We can write the derivative of z with respect to t using the chain rule:
We evaluate the partial derivatives of x, y with respect to t:
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