# Tagged Questions

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

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### If $s(x)= \int \sqrt{1+ \Big(\frac{dy}{dx}\Big)^2} dx$, what is $x(s)$?

$s(x)$ is the formula for arc length of a function $f(x)=y$. In the book I'm studying, curvature is defined as the instantaneous rate of change of direction (inclination of angle $\theta$) with ...
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### Use L'Hopital's rule to show that u′(t) = −λ u(t) (question from a Probability course)

I'm currently in a probability course and my professor suggested this question: Consider a continuous and differentiable function u(t) such that u(t + s) = u(t)u(s), for any s ∈ R and t ∈ R. This ...
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### Df(x) of $f:\mathbb R^{n^2}\rightarrow\mathbb R^{n^2}$

I am a bit a confused about finding $Df(x)$ of functions like $f:\mathbb R^{n^2}\rightarrow\mathbb R^{n^2}$. For example the derivative of the function $f:M_n(\mathbb R) \rightarrow Sym_n(\mathbb R)$ ...
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### Given Position equation Solve for t

This is calculus, and here is given information: Position of a spaceship at t hours after leaving planet is $$s(t)=.004t^3 + 400t$$ in thousands of miles. The distance between planet and destination ...