Question

Differentiate log (1 + x^2) with respect to tan^-1 x.​

Answer 1

log(1+x  

2

) with respect to tan  

−1

x

Let u=log(1+x  

2

)

  v=tan  

−1

x

dx

du

​  

=  

1+x  

2

 

2x

​  

 

dx

dv

​  

=  

1+x  

2

 

1

​  

 

dx

du

​  

 

dx

du

​  

 

​  

=  

1+x  

2

 

1

​  

 

(1+x  

2

)

2x

​  

 

​  

 

dv

du

​  

=  

(1+x  

2

)

2x

​  

×(1+x  

2

)

dv

du

​  

=2x