partial derivatives of a harmonic function are harmonic
105264
Why are partial derivatives of a harmonic function also harmonic?
31672
$L^p$-norm of the gradient of a harmonic function.
11205
Computing second partial derivative with polar coordinates
135941
Derivative of $|x|^\alpha$
44016
Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?
56936
$\frac{\partial f_i}{x_j}=\frac{\partial f_j}{x_i}\implies(f_1,\ldots,f_n)$ is a gradient
100007
Express partial derivatives of second order (and the Laplacian) in polar coordinates
151297
Second order partial of $f(x,y)=\frac{xy(x^2-y^2)}{x^2+y^2}$
42302
Use of Holder inequality in gradient estimate for harmonic function.
57677
Decomposition of Harmonic function into sum of holomorphic and anti-holomorphic function
91359
Are these mixed partial derivatives equal?
156536
Defining functions as derivatives
89057
How does one properly define the derivative of one operator-valued function?
59165
Derivative of a linear transformation.
144323
Differentiation of a function
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
12488
Show that $\frac{uu_x + vv_x}{u^2 + v^2}$ is harmonic.