Question

How do you differentiate `F(x) = (x)arctan x - (Ln ((x^2)+1))/2`?

Answer 1

`F'(x)=arctanx`

Explanation:

We have to use the product rule on `xarctanx` and the chain rule on `1/2ln(x^2+1)`:

`F(x)=xarctanx-1/2ln(x^2+1)`

`F'(x)=(d/dxx)arctanx+x(d/dxarctanx)-1/2(1/(x^2+1))(d/dx(x^2+1))`

`F'(x)=arctanx+x(1/(1+x^2))-1/2(1/(1+x^2))(2x)`

`F'(x)=arctanx+x/(1+x^2)-x/(1+x^2)`

`F'(x)=arctanx`