Question

f(x )=ln(1+x²)求导数

Answer 1

f(x)=ln(x+√1+x^2)
f'(x)=1/(x+√(1+x^2)
*(x+√1+x^2)'
=1/(x+√(1+x^2)*(1+(√1+x^2)'
=1/(x+√(1+x^2)*(1+1/2*√(x^2+1)
*(x^2)')
=1/(x+√(1+x^2)*(1+1/2*√(x^2+1)
*2x)
=(1+x/√(x^2+1))/(x+√(1+x^2)
分子分母乘x-√(1+x^2)
=(1+x/√(x^2+1)(x-√(x^2+1)/(x^2-1-x^2)
=(1+x/√(x^2+1)(√(x^2+1)-x)
=√(x^2+1)-x+x-x^2/√(x^2+1)
=√(x^2+1-供籂垛饺艹祭讹熄番陇x^2√(x^2+1)/(x^2+1)
=√(x^2+1)(1-x^2/(x^2+1))
=√(x^2+1)(x^2+1-x^2)/(x^2+1)
=√(x^2+1)/(x^2+1)

Answer 2

如图所示，注意复合函数的导数的求导法则，满意请采纳。