Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users

Dashboard
Notifications
Mark all as read
Q&A

Differentiating a series expansion of an arbitrary function

+0
−0

Differentiate $F(x)=f(x)+(a+h-x)f'(x)+\frac{(a+h-x)^2}{2!}f''(x)+... + \frac{(a+h-x)^{n-1}}{(n-1)!}f^{(n-1)}(x)+k(a+h-x)^m$

I was trying to solve it following way.

$$F'(x)=f'(x)-f'(x)+(a+h-x)f''(x)-(a+h-x)f''(x)+\color{blue}{\frac{(a+h-x)^2}{2!}f'''(x)}+\frac{\color{red}{(n-1)}(a+h-x)^{n-2}}{(n-1)!} f^{(n-1)}x+\frac{(a+h-x)^{n-1}}{(n-1)!}f^{(n)}(x)+km(a+h-x)^{m-1}(-1)$$

$$= \frac{(a+h-x)^2}{2!}f'''(x)+\frac{(n-1)(a+h-x)^{n-2}}{(n-1)!}f^{(n-1)}(x)+\frac{(a+h-x)^{n-1}}{(n-1)!}f^{(n)}(x)-km(a+h-x)^{m-1}$$

I had marked(with Red color) something. According to my book, it shouldn't be there. But, according to my calculation it should be there.

They didn't write the blue line also but, I don't have any problem on it cause, they put that as extra function (used ... for that function).


The function I said to differentiate.

enter image description here

The way they differentiate.

enter image description here


If it canceled with $(n-1)!$ than, why it didn't disappear from both side (numerator and denominator)? Even, why the value decreased if it canceled?

In last line $$\frac{(a+h-x)^{n-2}}{(n-2)!} f^{(n-1)}x$$ where it had gone? I can merge the denominator to $\frac{(a+h-x)^{n-1}}{(n-1)!}f^{(n)}(x)$ but, how to merge numerator?

Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

0 comment threads

1 answer

+0
−0

$$\frac{n-1}{(n-1)!}$$ $$=\frac{n-1}{(n-1)(n-2)!}$$ $$=\frac{1}{(n-2)!}$$

Why does this post require moderator attention?
You might want to add some details to your flag.

0 comment threads

Sign up to answer this question »