Differentiation of Piecewise Functions Describe how you would differentiate a piecewise function. Use your approach to find the first and second derivatives of . Explain why does not exist.
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Proof In Exercises 51 and 52, prove the identity, where R is a simply connected region with piecewise smooth boundary C. Assume that the required partial derivatives of the scalar functions f and g are continuous. The expressions and are the derivatives in the direction of the outward normal vector N of C and are defined by and .
Greenās second identity:
(Hint: Use Greenās first identity from Exercise 51 twice.)
Proof In Exercises 51 and 52, prove the identity, where R is a simply connected region with piecewise smooth boundary C. Assume that the required partial derivatives of the scalar functions f and g are continuous. The expressions
g are the derivatives in the direction of the outward normal vector N of C and are defined by
Greenās first identity:
[Hint: Use the second alternative form of Greenās Theorem and the property div
