What is (\partial)/(\partial x)(e^x-x^2arctan(x)) ?

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

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(\partial)/(\partial x)(e^x-x^2arctan(x))

\frac{\partial}{\partial x} (e^{x} - x^{2} arctan (x))

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

Solution steps

\frac{\partial}{\partial x} (e^{x} - x^{2} arctan (x))

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{x}) - \frac{\partial}{\partial x} (x^{2} arctan (x))

\frac{\partial}{\partial x} (e^{x}) = e^{x}

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

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

Simplify

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

\frac{6 ( t + 1 ) d y}{d t} - 5 y = 5 t, y (0) = 4

g (x) = - x

\frac{d y}{d x} = 2 y - x y^{2}

\int - \frac{5}{12 - 12 x ^{2}} d x

\frac{d}{d x} (\frac{x ^{2} + 5}{x ^{2} + 6 x})

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