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Popular >

derivative of arctan(e^x+1)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from-1 to 2 of (x^2-x-2)

\int_{- 1}^{2} (x^{2} - x - 2) d x

limit as x approaches-5 of (x^2)/(5-x)

x \to - 5 lim (\frac{x ^{2}}{5 - x})

derivative of 9/(x^4)

\frac{d}{d x} (\frac{9}{x ^{4}})

area 3x^2,-3x+6,-4,2 area

3 x^{2}, - 3 x + 6, - 4, 2

limit as x approaches 0+of (x+92)/x

x \to 0 + lim (\frac{x + 92}{x})

Frequently Asked Questions (FAQ)

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