Solution Found!
Explain why or why not Determine whether the
Chapter 12, Problem 47E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
(a) \(\frac{\partial}{\partial x}\left(y^{10}\right)=10 y^{9}\)
(b) \(\frac{\partial^{2}}{\partial x \partial y}(\sqrt{x y})=\frac{1}{\sqrt{x y}}\)
(c) If f has continuous partial derivatives of all orders, then \(f_{x x y}=f_{y x x}\)
Questions & Answers
QUESTION:
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
(a) \(\frac{\partial}{\partial x}\left(y^{10}\right)=10 y^{9}\)
(b) \(\frac{\partial^{2}}{\partial x \partial y}(\sqrt{x y})=\frac{1}{\sqrt{x y}}\)
(c) If f has continuous partial derivatives of all orders, then \(f_{x x y}=f_{y x x}\)
ANSWER:Problem 47E
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a.
b.
c. If f has continuous partial derivatives of all orders, then fxxy = fyxx.
A)
This Statement is Correct
Solution: