Răspuns:
Aplicui formula
(arcsin u) `= u `/√(1-u²) unde
u(x)=x/√(1+x²)
u `(x)=[x`*√(1+x²)-x*√(1+x²)`]/√(1+x²)²=
(√(1+x²)-x*2x/2√(1+x²)/(1+x²)=
(√(1+x²)-x²/√(1+x²))/(1+x²)=
(√(1+x²)²-x²)/(1+x²)*√(1+x²)=
(1+x²-x²)/(1+x²)√(1+x²)=1/(1+x²)√(1+x²)
---------
√(1-u²x)=√[1-(x/√1+x²)²=
√[1-x²/(1+x²)=√(1+x²-x²)/(1+x²)=
1/√(1+x²)
u `(x)/u(x)=1/(1+x²)*√(1+x²):(1/√(1+x²)=
√(1+x²)/(1+x²)*√(1+x²)=
1/(1+x²)
Explicație pas cu pas:
