Question
In Exercises 7 through 10, apply Definition 19.4.2 to find each of the partial derivatives.$$f(x, y, z)=x^{2} y-3 x y^{2}+2 y z ; D_{2} f(x, y, z)$$
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4.2: The partial derivative of a function f(x, y, z) with respect to the second variable y is denoted by D2f(x, y, z) and is defined as: D2f(x, y, z) = lim(h->0) [f(x, y+h, z) - f(x, y, z)] / h Now, let's apply this definition to find the partial derivative Show more…
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In Exercises $3-10,$ use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables. $$ \frac{\partial f}{\partial s}, \frac{\partial f}{\partial r} ; f(x, y, z)=x y+z^{2}, x=s^{2}, y=2 r s, z=r^{2} $$
DIFFERENTIATION IN SEVERAL VARIABLES
The Chain Rule
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