# Questions tagged [derivatives]

Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

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### Math 110C, Multivariable Calculus, Absolute Max and Min for 2 Variables

Find the absolute maximum and minimum values of $f$ on the set $D$. $f(x,y)=x^2+y^2-2x$, $D$ is the closed triangular region with vertices (2,0),(0,2),and(0,-2). First, I found the first partial ...
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### almost-Newton flows are Newton flows where the chain-rule is 'forgotten', yet its solutions are roots of f anyway, when does this work?

The differential equation for the Newton flow $z (t)$ of $f (t)$ is given by \begin{equation} \dot{z} (t) = - \frac{f (z (t))}{\frac{d}{d t} f (z (t))} = - \frac{f (z (t))}{\dot{f} (z (t)) \dot{z} ...
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### Pls help me find f(x).I am stuck with two functions here. [closed]


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### Determine $\frac{\partial\frac{\partial x}{\partial a}}{\partial b}$ from $f(x,a,b)=0$ with implicit function theorem

Say I have the following: $$f(x,a,b)=0\qquad\text{(1)}$$ Applying the implicit function theorem I get something like this: $$\frac{\partial x(a,b)}{\partial a}=\frac{f'_a}{f''_x}\qquad\text{(2)}$$ ...
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### What is the derivative of this quadratic form?

Given the quadratic form $f(x)=x^TK(x)x$, what is its derivative ? Thanks in advance. Edit : using Golden_Ratio suggestion I get : $f’(x) = (K(x)+K^T(x))x+2K’(x)x^TK(x)$ . Is it correct?
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### How to calculate $\lim_{x\searrow 0}f'(x)$, where $f(x)=(\sin x)^{\cos x} + (\cos x)^{\sin x}$, without Taylor series or aproximations

Let $f:[0, \frac{\pi}{2})\to\mathbb{R},\ f(x)=(\sin x)^{\cos x} + (\cos x)^{\sin x}$. Calculate $f'_d(0)$, the limit of the derivative in $x=0$. I've seen this limit being computed before on this ...
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### How to calculate the $\nabla \cdot \epsilon\nabla V = \nabla \epsilon \cdot \nabla V+\epsilon \nabla \cdot \nabla V$ [duplicate]

How to calculate the $\nabla \cdot \epsilon\nabla V = \nabla \epsilon \cdot \nabla V+\epsilon \nabla \cdot \nabla V$ I know the calculation of inner product and $\nabla$ ,but when if i have to ...