A general form derivative problem

  • Thread starter EngWiPy
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  • #1
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Main Question or Discussion Point

Hello,
Suppose that [tex]f(x)=g\left(h(x)\right)[/tex], then can we write [tex]f^{(n)}(x)=g^{(n)}\left(h(x)\right)\times k\left(h(x)\right)[/tex]??
Note: [tex]f^{(n)}(x)=\frac{d^n\,f(x)}{dx^n}[/tex].
Regards
 
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  • #2
mathman
Science Advisor
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Hello,
Suppose that [tex]f(x)=g\left(h(x)\right)[/tex], then can we write [tex]f^{(n)}(x)=g^{(n)}\left(h(x)\right)\times k\left(h(x)\right)[/tex]??
Note: [tex]f^{(n)}(x)=\frac{d^n\,f(x)}{dx^n}[/tex].
Regards
No.
f'(x)=g'(h(x))h'(x)
f''(x)=g''(h(x))[h'(x)]2+g'(h(x))h''(x)

It doesn't look anything like what you are proposing.
 
  • #3
Vid
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  • #4
1,367
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Thanks for replying. Let me to be more specific now, I think it may simplify the general form as given by Vid. I want to find the [tex]n^{th}[/tex] derivative with repect to [tex] s [/tex]of the following function:

[tex]\frac{\Psi(a,b;\varphi^-(s))-\Psi(a,b;\varphi^+(s))}{\sqrt{(\zeta-s)^2-4\beta^2}}[/tex]​

where

[tex]\varphi^{\pm}=(\zeta-s)\pm \sqrt{(\zeta-s)^2-4\beta^2}[/tex]​

and

[tex]\frac{\partial^n}{\partial z^n}\Psi(a,b;z)=(-1)^n\,(a)_n\Psi(a+n,b+n;z)[/tex]​

where

[tex](a)_n=a(a+1)\ldots (a+n-1)[/tex]​
 

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