Question

求函数y=e∧arctan√x的导数

Answer 1

y'=e^arctan√x*(arctan√x)'

=e^arctan√x*1/(1+x)*(√x)'

=e^arctan√x*1/(1+x)*1/(2√x)

扩展资料：

商的导数公式：

(u/v)'=[u*v^(-1)]'

=u' * [v^(-1)] +[v^(-1)]' * u

= u' * [v^(-1)] + (-1)v^(-2)*v' * u

=u'/v - u*v'/(v^2)

通分，易得

(u/v)=(u'v-uv')/v²

常用导数公式：

1、c'=0

2、x^m=mx^(m-1)

3、sinx'=cosx，cosx'=-sinx，tanx'=sec^2x

4、a^x'=a^xlna，e^x'=e^x

5、lnx'=1/x，log(a，x)'=1/(xlna)

6、(f±g)'=f'±g'

7、(fg)'=f'g+fg'

Answer 2

y'=e^arctan√x*(arctan√x)'
=e^arctan√x*1/(1+x)*(√x)'
=e^arctan√x*1/(1+x)*1/(2√x)