What is the derivative of arcsinh(sqrt(x)) ?

The derivative of arcsinh(sqrt(x)) is 1/(2sqrt(x)\sqrt{x+1)}

What is the first derivative of arcsinh(sqrt(x)) ?

The first derivative of arcsinh(sqrt(x)) is 1/(2sqrt(x)\sqrt{x+1)}

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\frac{d}{d x} (arcsinh (x))

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

Solution steps

\frac{d}{d x} (arcsinh (x))

Apply the chain rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

Simplify

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

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

d er i v a t i v e x^{4} - 3 x

x \to - 0.1 lim (\frac{e ^{x} - 1}{x})

\frac{d x}{d t} = 7 x t^{4}

\frac{d}{d x} (- \frac{18}{a x})

x \to 0 + lim (sin (x) \cdot ln (2 x))

What is the derivative of arcsinh(sqrt(x)) ?
The derivative of arcsinh(sqrt(x)) is 1/(2sqrt(x)\sqrt{x+1)}
What is the first derivative of arcsinh(sqrt(x)) ?
The first derivative of arcsinh(sqrt(x)) is 1/(2sqrt(x)\sqrt{x+1)}