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

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

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

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

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\frac{d}{d x} (e^{a r c t a n (x)})

\frac{e ^{a r c t a n (x)}}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (e^{a r c t a n (x)})

Apply the chain rule:

e^{a r c t a n (x)} \frac{d}{d x} (arctan (x))

= e^{a r c t a n (x)} \frac{d}{d x} (arctan (x))

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

= e^{a r c t a n (x)} \frac{1}{x ^{2} + 1}

Simplify

e^{a r c t a n (x)} \frac{1}{x ^{2} + 1} : \frac{e ^{a r c t a n (x)}}{x ^{2} + 1}

= \frac{e ^{a r c t a n (x)}}{x ^{2} + 1}

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