Question

高等数学

计算下列函数的导数
1. y=sin(2x/ (1+x^2))
2. y=In(x+更号（1+x^2）)
要过程 谢谢

Answer 1

1. y'=cos(2x/ (1+x²))*(2x/ (1+x²))'
=cos(2x/ (1+x²))*(2(1+x²)-2x*2x) / (1+x²)²
=2(1-x²) / (1+x²)² cos(2x/ (1+x²))

2. y'=(x+√(1+x²))'/(x+√(1+x²))
=(1+2x/2√(1+x²))/(x+√(1+x²))
=(x+√(1+x²))/((x+√(1+x²))*√(1+x²))
=1/√(1+x²)