What is the derivative of arcsinh(sqrt(3x)) ?

The derivative of arcsinh(sqrt(3x)) is (sqrt(3))/(2sqrt(x)\sqrt{3x+1)}

What is the first derivative of arcsinh(sqrt(3x)) ?

The first derivative of arcsinh(sqrt(3x)) is (sqrt(3))/(2sqrt(x)\sqrt{3x+1)}

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

\frac{3}{2 x 3 x + 1}

Solution steps

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

Simplify

arcsinh (3 x) : arcsinh (3 x)

= \frac{d}{d x} (arcsinh (3 x))

Apply the chain rule:

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

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

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= \frac{1}{( 3 x ) ^{2} + 1} \cdot \frac{3}{2 x}

Simplify

\frac{1}{( 3 x ) ^{2} + 1} \cdot \frac{3}{2 x} : \frac{3}{2 x 3 x + 1}

= \frac{3}{2 x 3 x + 1}

\int x e^{9 x} d x

\int e^{\frac{z}{y}} d z

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

\frac{\partial}{\partial x} (1 + x^{2} y - x y)

\frac{d}{d t} (2 t + 2)

What is the derivative of arcsinh(sqrt(3x)) ?
The derivative of arcsinh(sqrt(3x)) is (sqrt(3))/(2sqrt(x)\sqrt{3x+1)}
What is the first derivative of arcsinh(sqrt(3x)) ?
The first derivative of arcsinh(sqrt(3x)) is (sqrt(3))/(2sqrt(x)\sqrt{3x+1)}