Derivation of complex abstract functions

Derivation of complex abstract functions - Printable Version

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Derivation of complex abstract functions - yangyongkang - 04-04-2020 02:53 PM

The new version of CAS has improved many functions such as this function

Code:

(diff(∫(∫(f(sqrt(x^2+y^2)),x,-(sqrt(t^2-y^2)),sqrt(t^2-y^2)),y,-t,t),t,3)|(t>0))

Got

Code:

2*π*t*diff(f(t),t,2)+4*π*diff(f(t),t)

this is correct.

But there are errors in two functions。

Code:

∂(∫((-(f(((a^2+a*x)/x)))+f(((a^2+x^4)/x^2)))/x,x,1,a),a)

Got

Code:

(-(f(2*a))+f(a^2+1))/a

Code:

∂((f((a^2/x^2)+x^2)-(f((a^2/x)+x)))/x,x)

Got

Code:

(f((a^2+x^2)/x)-(f((a^2+x^4)/x^2)))/x^2

Obviously, both are wrong