What is the derivative of arcsinh((2x+5/(sqrt(23)))) ?

The derivative of arcsinh((2x+5/(sqrt(23)))) is 1/(sqrt(x^2+5x+12))

What is the first derivative of arcsinh((2x+5/(sqrt(23)))) ?

The first derivative of arcsinh((2x+5/(sqrt(23)))) is 1/(sqrt(x^2+5x+12))

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\frac{d}{d x} (arcsinh (\frac{2 x + 5}{23}))

\frac{1}{x ^{2} + 5 x + 12}

Solution steps

\frac{d}{d x} (arcsinh (\frac{2 x + 5}{23}))

Apply the chain rule:

\frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \frac{d}{d x} (\frac{2 x + 5}{23})

= \frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \frac{d}{d x} (\frac{2 x + 5}{23})

\frac{d}{d x} (\frac{2 x + 5}{23}) = \frac{2}{23}

= \frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \cdot \frac{2}{23}

Simplify

\frac{1}{( \frac{2 x + 5}{23} ) ^{2} + 1} \cdot \frac{2}{23} : \frac{1}{x ^{2} + 5 x + 12}

= \frac{1}{x ^{2} + 5 x + 12}

\frac{d}{d x} (- 3 x)

- \frac{8}{x ^{2}} - \frac{8}{x}

\int_{2}^{3} \frac{20}{3 - x} d x

\frac{\partial}{\partial x} (3 cos (x y))

What is the derivative of arcsinh((2x+5/(sqrt(23)))) ?
The derivative of arcsinh((2x+5/(sqrt(23)))) is 1/(sqrt(x^2+5x+12))
What is the first derivative of arcsinh((2x+5/(sqrt(23)))) ?
The first derivative of arcsinh((2x+5/(sqrt(23)))) is 1/(sqrt(x^2+5x+12))