What is the derivative of arctan(x+x/(1+x^2)) ?

The derivative of arctan(x+x/(1+x^2)) is 2/((x^2+1)^2)

What is the first derivative of arctan(x+x/(1+x^2)) ?

The first derivative of arctan(x+x/(1+x^2)) is 2/((x^2+1)^2)

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Popular >

\frac{d}{d x} (arctan (x) + \frac{x}{1 + x ^{2}})

\frac{2}{( x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (arctan (x) + \frac{x}{1 + x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arctan (x)) + \frac{d}{d x} (\frac{x}{1 + x ^{2}})

\frac{d}{d x} (arctan (x)) = \frac{1}{x ^{2} + 1}

\frac{d}{d x} (\frac{x}{1 + x ^{2}}) = \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}}

= \frac{1}{x ^{2} + 1} + \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}}

Simplify

\frac{1}{x ^{2} + 1} + \frac{1 - x ^{2}}{( 1 + x ^{2} ) ^{2}} : \frac{2}{( x ^{2} + 1 ) ^{2}}

= \frac{2}{( x ^{2} + 1 ) ^{2}}

(tan (x)) (x)

\frac{\partial}{\partial x} (ln (2 x + 5 y))

y^{^{''}} + 2 y^{^{'}} + \frac{3}{4} y = 0

\int 3 - \frac{1}{x ^{4}} d x

(ln (1))^{^{'}}

What is the derivative of arctan(x+x/(1+x^2)) ?
The derivative of arctan(x+x/(1+x^2)) is 2/((x^2+1)^2)
What is the first derivative of arctan(x+x/(1+x^2)) ?
The first derivative of arctan(x+x/(1+x^2)) is 2/((x^2+1)^2)