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Popular >

derivative of 2arctan(e^x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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}

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

Simplify

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

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

Popular Examples

derivative of 8(x+2^{3/2})

\frac{d}{d x} (8 (x + 2)^{\frac{3}{2}})

derivative of-2x^4+3x^3-x^2

\frac{d}{d x} (- 2 x^{4} + 3 x^{3} - x^{2})

implicit (dy)/(dx),40x^{1/3}y^{2/3}=480 implicit derivative

\frac{d y}{d x}, 40 x^{\frac{1}{3}} y^{\frac{2}{3}} = 480

integral of (2x)/((x-1)(x-2))

\int \frac{2 x}{( x - 1 ) ( x - 2 )} d x

integral of ((x^2+3x+1))/x

\int \frac{( x ^{2} + 3 x + 1 )}{x} d x

Frequently Asked Questions (FAQ)

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