Linked Questions
10 questions linked to/from Higher-order partial derivatives w.r.t. variable raised to some power
2
votes
1
answer
696
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Derivative w.r.t another function [duplicate]
Find $\frac{dv}{du}$ if $v=\sin^{-1}\frac{2x}{1+x^2}$ w.r.t $u=\tan^{-1}\frac{2x}{1-x^2}$
$$v=\sin^{-1}\frac{2x}{1+x^2}=\begin{cases}2\tan^{-1}x&\text{, if }|x|<1\\
\pm\pi-2\tan^{-1}x&\...
- 311
1
vote
1
answer
498
views
Take the derivative of a function of time by another function of time [duplicate]
What I am asking could seem simple but I couldn't find a solution nor here nor in google.
I want to take the derivative of a function by another function.
Let say I have two functions of time ...
- 87
0
votes
0
answers
192
views
Derivative of a function with respect to another function [duplicate]
I have a question, I would be grateful if someonr helped me.
Suppose I have these functions:
te[x_] := x^2
te1[x_] := te[x] x
How can I numericaliy ...
- 65
0
votes
0
answers
38
views
Derivative where the variable is a function, e.g. D[x^4,x^2] [duplicate]
How can I express in MMA a derivative if the variable is a function?
Example:
The first derivative of $x^4$ with respect to $x^2$, would be
$\dfrac{\mathrm{d}{x^4}}{\mathrm{d}{x^2}}=2x^2$ ?
...
- 593
7
votes
2
answers
1k
views
Differentiate w.r.t. squared variable
Is it possible to differentiate symbolically w.r.t. some squared quantity in Mathematica? Evaluating something like
D[x^4 + 2 x^2 + 6, x^2]
gives the error ...
- 1,311
2
votes
3
answers
443
views
How can I take derivatives recursively in Mathematica? [closed]
Let's say I have the function
f[x_]:=x^50
I want to take one derivative and multiply the result by x recursively. That is, I want to
...
- 553
1
vote
1
answer
901
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How to write a general derivative function of parametric equation?
Here I see a mathematical method for finding higher order derivatives of parametric equations:
$$\begin{equation}
\left\{
\begin{aligned}
x & = f(t) \\
y & = g(t)
\end{aligned}
\right.
\end{...
2
votes
1
answer
409
views
Can DSolve give results in parametric form?
Can DSolve give results in parametric form?
For example the cycloid equation is:
DSolve[{(x'[t])^2 == r/x[t] - 1}, x[t], t]
And the solution is usually given in ...
- 6,837
0
votes
0
answers
575
views
How to differentiate with respect to a function
I have some complicated expression, let's call it $X_n$, for which I don't have a closed form, but I do have a recurrence relation. It is given in terms of some functions $u(x,y),$ $v(x,y),$ and ...
- 101
2
votes
2
answers
69
views
How to get derivation of a function with respect to another function?
I often have this need: I have some functions that have the same variable and have inclusion relationships, like this.
f[t_] := t^2 + 1
g[t_] := Exp[-I Sin[f[t]]]
...
