Question

What is the derivative of `f(x) = (arctan (x/2)) + ((5x-1)/(2(x^2) + 4))`?

Answer 1

`f'(x)=2/(4+x^2)+(-10*x^2+4x+20)/(2*x^2+4)^2`

Explanation:

Note that
`(arctan(x))'=1/(1+x^2)`
so we get

`f'(x)=1/(1+x^2/4)*1/2+(5*(2x^2+4)-(5*x-1)*4x)/(2x^2+4)^2`

so we get

`f`(x)=2/(4+x^2)+(-10*x^2+4x+20)/(2*x^2+4)^2`