What is the (arctan(e^x))^' ?

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

What is the first (arctan(e^x))^' ?

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

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(arctan (e^{x}))^{^{'}}

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

Solution steps

(arctan (e^{x}))^{'}

Apply the chain rule:

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

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

(e^{x})^{'} = e^{x}

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

Simplify

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

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

\frac{d}{d x} (arccsc (2 x + 1))

\int (sin (x))^{3} (cos (x)) d x

x \to - 1 lim (\frac{1}{x + 1})

x \to 0 lim (e^{7 x})

\int arccos (7 x) d x

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