# 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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### Partial derivative of a composite function, given the definition of one of the functions [closed]

I need to find $\frac{∂f}{∂x}$ of $f(x) = \frac{1}{2}\phi(wx+b)$ where $\phi(x)=x^2$ I'm looking at something like $\frac{∂f}{∂x} = \frac{∂f}{∂\phi}\frac{∂\phi}{∂x}$, but I'm not sure how to do it ...
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### How can we expand $(f(x)*d/dx)^n$? And why? [closed]

Which one is the correct expansion of $(f(x)d/dx)^2$? $(f(x))^2 (d^2/dx^2)$ or $(f(x)d/dx)(f(x)d/dx)$? And why?
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### Partial derivatives in scalar field taylor expansion

$\newcommand{\v}[1]{\mathbf{#1}} \newcommand{\abs}[1]{\lvert#1\rvert} \newcommand{\dd}[1]{\mathrm{d}#1}$ In our lecture notes we derived the following formula for the Taylor expansion of a scalar ...
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I have the following relationship between variables: $$\varepsilon = \Psi -\frac{v^2}{2}\tag{1}$$ A while back, I had an integral with respect to $v$ and I wanted to convert it to an integral with ...