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Popular >

derivative of arctan(e^x)

Solution

derivative of

arctan (e^{x})

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}

Popular Examples

(dx)/(dt)= 5/(xe^{t+6x)}

\frac{d x}{d t} = \frac{5}{x e ^{t + 6 x}}

integral of t/2

\int \frac{t}{2} d t

derivative of x^2+2x+1

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

integral from 1 to 2 of integral from 2 to 4 of xy^3(e^2)^{x^2y^2}

\int_{1}^{2} \int_{2}^{4} x y^{3} (e^{2})^{x^{2} y^{2}} d x d y

integral of xcos(2x)+x^3+4x+2+sec(2x)

\int x cos (2 x) + x^{3} + 4 x + 2 + sec (2 x) d x

Frequently Asked Questions (FAQ)

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