# Tagged Questions

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

1answer
14 views

### How is the class related to derivability?

Good evening to everyone. I have a question where they require me to find the derivability. After I read the answer sheet I saw that the function has the class $C^1$. How is the class related to ...
1answer
28 views

### Why $\frac{d}{dt}f(x+t(y−x))<0$ if $x < y, f(y) < f(x)$

Here excerpt from a book: Аssume that $f$ satisfies $\nabla f(x) \ge 0$ for all $x$, but is not nondecreasing, i.e., there exist $x,y$ with $x < y$ and $f(y) < f(x)$. By ...
2answers
92 views

### $f: \Bbb R^2 \to \Bbb R$ whose partials exist. Show: $\partial _xf \:\:\mathrm{continuous} \Rightarrow f \:\:\mathrm {differentiable}$

Let $f: \Bbb R^2 \to \Bbb R$ be a function whose partial derivatives exist. Now i have to show: $$\partial _xf \:\:\mathrm{continuous} \Rightarrow f \:\:\mathrm {differentiable}$$ Any tipps on how ...
2answers
51 views

1answer
37 views

### Using the chain rule for cos and sin functions

I am having issues with derivatives containing chain rules. I know there is multiple threads already but after reading a few, I still find myself confused. I also checked the actual answer following a ...
1answer
51 views

### Definition of derivative to calculate $x\sqrt{|x|}$ at $x=0$

So the question says use the definition of the derivative to calculate the derivative of $x\sqrt{|x|}$ at $x=0$. I understand the definition of derivative but have no idea where to go from there to ...
2answers
31 views

### Why is it true that $S'(t)/S(t) = d log(S(t)) / dt$?

I came across this identity in derivation of the hazard rate in survival analysis.
1answer
27 views

### Derivative of a characteristic polynomial at an eigenvalue

Let $p(\lambda)$ be the characteristic polynomial of an $n\times n$ matrix $A$. We know that the roots of $p(\lambda)$ are the eigenvalues of $A$, hence the sum of the roots of the polynomial (taking ...
0answers
33 views

### How would I find the nth derivative of a function, where n is imaginary? What about where n is not a constant? [duplicate]

Forgive me if this question has already been asked. I was unable to find anything relevant to this question. The $n$th derivative of a function, $f^n(x)$ is well-defined for $n\in\mathbb{Z}^+$. As ...
1answer
30 views

### What should i conclude from the following workout?

We know that for any value of $x$ other than $0$, $a^x\ne e^x$ where $a>e, a\in R^+$ but we do know that for some value of $p$, $$pa^x=e^x\ldots(1)$$ you see $p$ is a positive number because of ...
0answers
34 views

1answer
55 views

0answers
23 views

### Defining derivatives and integrals for hyperoperations > 2

Derivatives and Integrals are continuous generalizations of the Forward Difference and Summation additive operators respectively. We can do the same with multiplication and get multiplicative calculus ...
2answers
98 views

### Increasing function with $f'(x)=f(f(x))$ [duplicate]

Is there a strictly increasing function $f: \mathbb{R}\rightarrow \mathbb{R}$ such that $f'(x)=f(f(x))$ for all $x$?
1answer
53 views

### shifting integration variable and taking derivative seemingly giving problem

I am doing loop integral in quantum field theory, and an issue in shifting integration variable is giving me a problem. Let me illustrate with an example. I have an integral that looks approximately ...
2answers
17 views

### Evaluating a statement without calculating the indefinite integral

I'm cramming for a supplementary exam so you might see a ton of questions like these in the 48+ hours to come <3 The question is more of just a yes or no ; Evaluate the statement without ...
1answer
19 views

### Derivative of Incomplete Gamma Function

For the following incomplete Gamma function: $$Γ(1+d,A-c \ln x)=\int_{A-c\ln x}^{\infty}t^{(1+d)-1}e^{-t}dt$$ I am trying to calculate the derivative of $Γ$ with respect ...
1answer
53 views

0answers
34 views

### Understanding a calculation deduced for the function $\pi^{-s/2}\Gamma(s/2)\zeta(s)$

With my current knowledges I don't know if this is a bad question, but since I am interesting in this kind of calculations I want to ask you, if I was wrong or if if my statement is obvious. From ...
1answer
25 views

### How to calculate $∇(r^2/(2z(1+a/z^2)))$ in cylindrical coordinates

How to calculate $$∇\bigg(\frac{(ρ^2)}{2z(1+\frac{a}{z^2})}\bigg)$$ where the function is in cylindrical coordinates $$ρ^2=x^2+z^2$$ $$∇\bigg(\frac{x^2+z^2}{2z(1+\frac{a}{z^2})}\bigg)$$ Is the ...
2answers
28 views

### Sign of the derivative $-e^{\frac{1}{2x+2}}\left(sgn\left(x\right)+\frac{1-\left|x\right|}{2\left(x+1\right)^2}\right)$

Good morning to everyone. I have a problem with finding the sign of a derivative: $$\frac{d}{dx}f(x)=-e^{\frac{1}{2x+2}}\left(sgn\left(x\right)+\frac{1-\left|x\right|}{2\left(x+1\right)^2}\right)$$ ...
6answers
46 views

### Critical points of a cubic function

There is a function $x^3 - 6x^2 + 9x + 1$. Its critical points are $1$ and $3$. I am very confused, if these points are maximum and minimum points respectively or are both inflection points. Can ...