Tagged Questions
1
vote
2answers
143 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
4
votes
4answers
204 views
Differentiating space curves
I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by
...
4
votes
2answers
175 views
Define product derivative
How do I define the $n$th product derivative of a function in Mathematica?
The first product derivative $f^\ast$ of a function $f$ is
$$
f^\ast(x)=\exp\left(\frac{f^\prime(x)}{f(x)}\right)
$$
The ...
4
votes
2answers
916 views
How to find (numerical) value of a derivative at point?
I have the following function:
f[0, 0] = 0
f[x_, y_] := Exp[-(x^2 + y^2)^(-1)]
How do I find its partial derivatives at any given point, including $(0,0)$? This ...
7
votes
1answer
438 views
How to find the smallest root
I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
4
votes
3answers
308 views
Integrating with multiple indicator functions
I am trying to calculate an integral involving multiple indicator functions, such as:
$$ h(u,v,w) = -\int_0^1 J^{\prime\prime}(s) (I_{(0,s]}(u) - s)(I_{(0,s]}(v) - s)(I_{(0,s]}(w) - s)\, ...
