I wonder why and how it works. Please show me the steps, thanks
Why does the mixed partial derivative of $ sin(x)+sin(y)=0$
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$\begingroup$
calculus
ordinary-differential-equations
derivatives
partial-derivative
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2Think about what happens when you take $\partial^2/(\partial x\partial y)$ of any function of the form $f(x) + g(y)$. – 2017-02-02
2 Answers
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Let $f(x,y)=\sin(x)+\sin(y)$. Then $f_x(x,y)=\cos(x)$, which is independent of $y$. Therefore:
$f_{yx}(x,y)=0$.
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When you differeniate wrt. $x$, you have $\cos x$, which is constant wrt. $y$.