Tagged Questions

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

41 views

Proof with Lagrange theorem

The exercise is: Show, using Lagrange's theorem, that for $x \in [0, +\infty]$, we have $\frac{x}{1+x^2} \leq \arctan(x)$. I know how to apply Lagrange's theorem but my trouble is to find ...
55 views

28 views

calculus book recommendations [duplicate]

i want to learn single variable calculus i completed schooling and i love calculus for now i am focusing on single variable calculus i tried many books like Calculus - "A Complete Course 7th ed - R. ...
52 views

Finding the minimum and maximum values of f(x)=x+(1/x)

So basically the question is to find the minimum value of the sum $$f(x)=x+(1/x)$$ for any real number $x$. I differentiated the function and found the values of $x$ for which $f'(x)=0$ as $-1$ ...
60 views

Difference between partial derivative on R^d and the vector field d/dx

In Differential Geometry $\frac{\partial}{\partial x}$ is a vector field. Specifically, it is the coordinate induced basis vector field for the total space of the tangent bundle TM. The definition I ...
20 views

Derivative of relative position vector with respect to a vector

Dear Mathematics community members, I was trying to derive the forces arising from harmonic angle potential as in equation 3.112 of below link http://www.mbnexplorer.com/documentation/3-energy-and-...
63 views

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 ...
34 views

How to determine $a,n$ for $\lim\limits_{x\to 0} \frac{ax^n+e^{\sin x}-[1+\ln{(1+x^2)}]\cos{x}}{x^4}$ so that the limit is nonzero?

My thinking process is that, using L'hopital's rule, we differentiate the equation $4$ times and every time before differentiation, we record what $ax^n$ (or $nax^{n-1}$ or so on) equals to keep the ...
136 views

Why is $|x|^2$ differentiable?

Why should $|x|^2$ be differentiable? $$f(x)=|x|^2$$ Right limit: Since $h>0$, $$\lim_{h\to0^+}\frac{f(h)}{h}=\frac{(|h|)^2}{h}=\frac{h^2}{h}=h$$ Here h value will be positive. Left limit: ...
86 views

How to solve the antiderivative of $x\cos\left(x^3\right)$

What is the way to solve: $$\int x\cos\left(x^3\right)\space\text{d}x$$ Thanks, I've no idea how to start
Problem 1 On the curve $y=\frac{1}{1+x^2}$ find a point in which tangent line is parallel to the horizontal axis. My idea: Let's find $y'$. $$y'=\frac{-2x}{(1+x^2)^2}$$ If we want a tangent line to ...