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

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Answer 1 · 2018-06-03T10:52:07

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

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

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

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