What is the derivative of arccosh(e^{2x}) ?

The derivative of arccosh(e^{2x}) is (2e^{2x})/(sqrt(e^{2x)-1)sqrt(e^{2x)+1}}

What is the first derivative of arccosh(e^{2x}) ?

The first derivative of arccosh(e^{2x}) is (2e^{2x})/(sqrt(e^{2x)-1)sqrt(e^{2x)+1}}

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

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

\int x cos (ln (x)) d x

\int x^{14} e^{x^{3}} d x

\frac{\partial}{\partial x} (e^{x l n (y)})

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

2 x^{4} - 11 x^{2}

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