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6 questions with no upvoted or accepted answers
4 votes
0 answers
570 views

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 ...
You Xiao Ruan's user avatar
1 vote
0 answers
57 views

Determine lambda from a non-constant differentiable function of one variable

Suppose f is a non-constant differentiable function of one variable. Determine, with reasons, the value of $\lambda$ for which F(x, y) = f($\lambda x^{3}$ + y) satisfies the partial differential ...
samheihey's user avatar
  • 177
0 votes
1 answer
62 views

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 ...
Przemo's user avatar
  • 11.5k
0 votes
0 answers
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{...
Przemo's user avatar
  • 11.5k
0 votes
0 answers
34 views

Fractional derivatives in different coordinates

I wonder how fractional derivatives are defined in cylindrical coordinate? Does anyone have any idea?
OLIVER range's user avatar
0 votes
1 answer
204 views

Partial Fraction Expansion and Laplace Transform

I have some problem with my equation: $$y''+5y = 5e^{-5t} $$ And we got that y(0) = 1 and y'(0) = 2 It's too much to write but what I get is: $$ \frac{e^{-5t}}{6}+1.516676089\cdot \cos(0.989 - \sqrt{...
Fourierstudent's user avatar