What is the derivative of arctan(e^{x^2}+x^2) ?

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

What is the first derivative of arctan(e^{x^2}+x^2) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{x^{2}} + x^{2}) = e^{x^{2}} \cdot 2 x + 2 x

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

Simplify

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

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

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