# Tagged Questions

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

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### Differentiate equation with parenthesis

I have a problem. I'm studying calculus, but I don't have a good math background, so I have a problem: I don't know well how to differentiate an equation with parenthesis. The equation is the ...
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### Directional derivative of a differentable function

Is it always true, for a differentiable function $F:\mathbb{R}^N\rightarrow\mathbb{R}^M$, that its directional derivative along a direction $v\in\mathbb{R}^N$ is equal to the product $J_f\cdot v$, ...
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### What is the way to show the following derivative problem?

If $f$ is function twice differentiable with $|f''(x)|<1, x\in [0,1]$ and $f(0)=f(1)$, then $|f'(x)|<1$ for all $x\in [0,1]$ I have tried with Rolle's theorem, but fail
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### N-order differential equations

Suppose that we have n-order differential equation like $$h(x)=?$$ Is it possible to find a general solution for all n? $$(x^n+1).|h'(x)|^n=const.$$.
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### How to differentiate $\ln(a^x)$?

Can someone give me the process to differentiate this (with respect to $x$)? $$\ln(a^x)$$
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### How to differentiate x^(1/x)?

How to differentiate the following? $$x^{\frac{1}{x}}$$ (I know the answer is $\frac{1-\ln(x)}{x^{2-\frac{1}{x}}}$, but I do not understand how to get there) Attempt at solution I believe the ...
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### Fixed point, bounded derivative

Let $p\in\mathbb{N}$. Let $f:I\to\mathbb{R}$ differentiable in the closed interval $I$ (bounded or not), with $f(I) \subset I$, and let $g = f\circ f\circ \cdots \circ f = f^p$, where $\circ$ means ...
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### General chain rule help/ derivatives help.

I've been thinking too much about the chain rule and I've got myself in a muddle: Suppose $y=f(g(x))$, we can easily show that $\frac {dy}{dx} = f'(g(x))\cdot g'(x)$. I would ask please that ...
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