# Questions tagged [partial-derivative]

For questions regarding partial derivatives. The partial derivative of a function of several variables is the derivative of the function with respect to one of those variables, with all others held constant.

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### Lipschitz continuity and boundedness of derivatives.

Suppose $f(x)$ is a function that has derivative in the domain of our concern. We all know that if the derivative is bounded then $f$ is Lipschitz continuous. I was wondering if the above statement is ...
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### Multivariable Calculus, more specifically flux integral

So the question gives vector field $F(x,y,z)=(x^2,y^2,z^2)$ and it is flowing out of a sphere of $(x-1)^2+(y+1)^2+(z-2)^2 \leq 4$. Using Guass's rule, I transformed it into a triple integral while ...
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### What are some strategies for computing derivatives in matrix calculus?

In single variable calculus, the chain, product, and power rules are very straightforward. In vector calculus, it's a bit more involved. I frequently find myself having to do a lot of work to arrive ...
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### How to prove the result of an integral of partial derivatives

I have proof for question a but I cannot proof question b. How should I prove question b?
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### Manipulating derivatives

I am starting to learn some multivariable calculus and had a number of questions on some of the simplifications of differential expressions as I have not found a good resource that guides through. 1)...
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### Is the partial derivative of a constant always zero?

I'm trying to get my head round using the multivariable chain rule to find exact derivatives. For example I want to find the exact derivative(using partial derivatives) of, $$r^2=x^2+y^2$$ Where r is ...
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### geometric meaning of $\partial_{xy}f(x,y)?$ [duplicate]

I know that $\partial_x f(x,y)$ gives us the slope of the tangent line at the point (x,y) in the x direction. And $\partial_{xx}f(x,y)$ gives us the rate of change of that same slope. The same happens ...
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### Volume of the rectangular box with open top by enquality of geometric and hormonic means

A rectanglular box without lid made of 12 m^2 of cardboard. Find the volume by appropriate usage of inequalities of geometric and geometric means
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### Language and Algorithm to Take Derivatives in Function Notation

I want to algorithmically find derivatives and partial derivatives of expressions written in function notation. For example, I can type "d/dx f(x, y(x), g(x) * h(x))" directly into Wolfram Alpha, ...
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### Integrating unit vectors

If I want to find a function $V(r)$ such that ${\bf F} = -\nabla V$, where ${\bf F} = f(r)\hat{\bf r}$, how do I integrate ${\bf F}$ along the radial direction?