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Popular >

derivative of arctan(e^{2x})

Solution

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

Solution

\frac{2 e ^{2 x}}{e ^{4 x} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( e ^{2 x} ) ^{2} + 1} e^{2 x} \cdot 2 : \frac{2 e ^{2 x}}{e ^{4 x} + 1}

= \frac{2 e ^{2 x}}{e ^{4 x} + 1}

Popular Examples

laplacetransform 7t^5 laplace transform

7 t^{5}

integral of sec(x)(sec(x)+tan(x))

\int sec (x) (sec (x) + tan (x)) d x

integral of arctan(x)

\int arctan (x) d x

limit as y approaches infinity of (sqrt(y^2+2))/(5y-6)

y \to \infty lim (\frac{y ^{2} + 2}{5 y - 6})

x(dy)/(dx)-y=7x^3

x \frac{d y}{d x} - y = 7 x^{3}

Frequently Asked Questions (FAQ)

What is the derivative of arctan(e^{2x}) ?
The derivative of arctan(e^{2x}) is (2e^{2x})/(e^{4x)+1}
What is the first derivative of arctan(e^{2x}) ?
The first derivative of arctan(e^{2x}) is (2e^{2x})/(e^{4x)+1}