What is the derivative of arcsinh(x^2) ?

The derivative of arcsinh(x^2) is (2x)/(sqrt(x^4+1))

What is the first derivative of arcsinh(x^2) ?

The first derivative of arcsinh(x^2) is (2x)/(sqrt(x^4+1))

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\frac{d}{d x} (arcsinh (x^{2}))

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

Solution steps

\frac{d}{d x} (arcsinh (x^{2}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of arcsinh(x^2) ?
The derivative of arcsinh(x^2) is (2x)/(sqrt(x^4+1))
What is the first derivative of arcsinh(x^2) ?
The first derivative of arcsinh(x^2) is (2x)/(sqrt(x^4+1))