All Questions
Tagged with partial-fractions derivatives
21
questions
0
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1
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69
views
If the third derivative of $\frac{x^4}{(x-1)(x-2)}$ is $\frac{-12k}{(x-2)^4}$ + $\frac{6}{(x-1)^4}$ then the value of k is? [closed]
In the answers I found on google, see this link, they converted the given function into a certain form? What is the process of that conversion (I understand it is a partial fraction of sorts, but how ...
- 21
0
votes
1
answer
62
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Higher order partial derivatives of a product of reciprocals of cumulative sums
This question is related to another question where we asked for evaluating a certain multi-dimensional integral. It turns out that that integral, from the question above, can be reduced to an action ...
- 11.5k
2
votes
2
answers
120
views
How to decompose $\frac{1+x}{\sqrt{(1-x)}}$ into partial fractions?
Basically homework help. The question (Problems of Calculus in One Variable, IA Maron, number 2.3.9(b)) is to find the derivative of the 100th order of the function
$$
y = \frac{1+x}{\sqrt{(1-x)}}
$$
...
- 93
0
votes
2
answers
178
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Finding nth derivative of $\frac{1}{x^4+4}$
I am supposed to find the nth order derivative of:
$$\frac{1}{x^4+4}$$
I tried to resolve into partial fractions. But it didn't work out for me.
Edit- where I am stuck
$$\frac{1}{x^4+4}=\frac{1}{(x-1+...
- 1,229
0
votes
1
answer
53
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Decompose into simple fractions $\frac{f'}{f}$
Let $f(x) = (x-a_1)(x-a_2)...(x-a_n)$.
Find a decomposition into simple fractions of $\frac{f'}{f}$.
Where $f'$ is a derivative of our polynomial.
As I understand, we have to find a pretty-format of $...
- 588
9
votes
3
answers
278
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Compute 100th derivative [duplicate]
A friend suggested me a rather tricky problem, namely find the $100^{th}$ derivative of
$$
f(x)=\frac{x^2+1}{x^3-x}.
$$
I have computed the zeroth derivative
$$
\frac{x^2+1}{x^3-x}
$$
and the first ...
- 193
3
votes
2
answers
88
views
$f(x) = \frac{4 + x}{2 + x - x^2}$, calculate $f^{(9)}(1)$
$f(x) = \frac{4 + x}{2 + x - x^2}$, calculate $f^{(9)}(1)$, where $f^{(9)}$ is the $9$-th derivative of $f$.
Domain of $f$ is $\mathbb{R} - \{-1, 2\}$. I've got that $f(x) = \frac{1}{1 - (-x)} + \...
- 583
0
votes
1
answer
39
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$2n$ th partial derivative of $\frac{1}{y(1+x^2)-1}$ with respect to $x$.
I need to find the $2n$ th derivative with respect to $x$ of the function $f = \frac{1}{y(1+x^2)-1}$. I tried differentiating util a pattern was founded, but that didn't happen.
I think the $x^2$ is ...
- 2,687
10
votes
1
answer
156
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A determinant involving a polynomial is $0$
Let $n \geq 2$ and $f:\mathbb{R} \to \mathbb{R}, \: f(x)=(x-x_1)(x-x_2)\dots(x-x_n)$ where $x_1,\dots, x_n$ are distinct real numbers. The matrix $A=(a_{ij})_{1 \leq i,j \leq n}$ is defined as follows:...
- 1,837
2
votes
3
answers
116
views
Formula for $1/f(x)$ where $f$ is a polynomial
Let $f$ be a polynomial having $n$ distinct real roots:
$$f(x)=(x-x_1)(x-x_2)\dots(x-x_n)$$
Prove that $$\frac{1}{f(x)}=\sum_{k=1}^n \frac{1}{f'(x_k)(x-x_k)}, \: \forall x \in \mathbb{R} - \{x_1,...
- 1,837
0
votes
0
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139
views
How do we compute higher order derivatives of a rational function?
Let $a \in (-1,1)$ and $x\in {\mathbb R}$ and consider a following sequence of rational functions:
\begin{eqnarray}
R^{(0)}[x]&:=& \frac{x (a x-1)}{a x-x^2+x-1}\\
R^{(1)}[x]&:=& -\frac{...
- 11.5k
0
votes
0
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34
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Fractional derivatives in different coordinates
I wonder how fractional derivatives are defined in cylindrical coordinate?
Does anyone have any idea?
- 11
4
votes
0
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569
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Find the derivative of integral $f(x)/(x^2(x-5)^7)$ when $f(x)$ is a quadratic function.
This question is quite tricky. It's for my Calculus 2 assignment and I can't seem to figure out how to integrate this function in order to get its derivative. I tried partial fractions, u-sub with x-5 ...
- 175
0
votes
2
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623
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Natural parameterization of the following curves:
I am having trouble finding the natural parameterization of these curves:
$$\alpha(t)=\left(\sin^2\left(\frac{t}{\sqrt{2}}\right),\frac{1}{2}\sin \left(t\sqrt{2}\right), \left(\frac{t}{\sqrt{2}}\...
- 2,876
0
votes
1
answer
37
views
How can I find derivatives of this function with respect to $U_i$ and $V_j$?
I have this objective function, I want to find its derivative with respect to $U_i$ and $V_j$, I don't know how should I approach these kind of functions, it would be helpful if any one could tell me ...
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