Science:Math Exam Resources/Courses/MATH200/December 2011/Question 02 (a)
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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. a) 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
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Hint 

To evaluate this partial derivative we need to use the chain rule. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. 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: And thus, 