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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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5

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Partial differentiation

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5.1  Using the appropriate properties of ordinary derivatives, perform the following.

(a)  Find all the first partial derivatives of the following functions f(x, y):

(i) x2y, (ii) x2 + y2 + 4, (iii) sin(x/y), (iv) tan–1(y/x),

(v) r(x, y, z) = (x2 + y2 + z2)1/2.

(b)  For (i), (ii) and (v), find ∂2f/∂x2, 2f/∂y2 and ∂2f/∂x∂y.

(c)  For (iv) verify that ∂2f/∂x∂y = 2f/∂y∂x.

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These are all straightforward applications of the ...

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