Найти производную функции y=

Question

Найти производную функции y=

Answer 1

Y`=(√(1+x²)/√(1-x²))`=((1+x²)^(1/2))`*√(1-x²)-√(1+x²)*(√1-x²)^(1/2))/(√(1-x²))²=
=(2x/(2*√(1+x²))*(√(1-x²)-(√1+x²)*(-2x)/(2*(√(1-x²))/(1-x²)=
=(x*√(1-x²))/(√(1+x²)+(x*(√1+x²))/(√(1-x²))/(1-x²)=
=(x*(√1-x²))²+x*(√(1+x))²)/√(1-x⁴))/(1-x²)=
=(x(1-x²)+x(1+x²)/(√(1-x⁴))/(1-x²)=((x-x³+x+x³)/(√(1-x⁴))/(1-x²)=
=2x/(√(1-x²)(√(1+x²)(1-x²)=2x/((1-x²)(^3/2)*(√(1+x²)).