What is (\partial)/(\partial x)(1+arctan(x)) ?

The answer to (\partial)/(\partial x)(1+arctan(x)) is 1/(x^2+1)

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(\partial)/(\partial x)(1+arctan(x))

\frac{\partial}{\partial x} (1 + arctan (x))

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

Solution steps

\frac{\partial}{\partial x} (1 + arctan (x))

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (arctan (x))

\frac{\partial}{\partial x} (1) = 0

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

= 0 + \frac{1}{x ^{2} + 1}

Simplify

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

What is (\partial)/(\partial x)(1+arctan(x)) ?
The answer to (\partial)/(\partial x)(1+arctan(x)) is 1/(x^2+1)