What is the derivative of arcsinh(sqrt(1-x^2)) ?

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

What is the first derivative of arcsinh(sqrt(1-x^2)) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (e^{- 2 t} cos (x))

\int a + b x d x

x \to 0 lim (\frac{3 ∣ x ∣}{x ^{2}})

\int \frac{( 65 x + 7 )}{( 8 x + 1 ) ( x - 1 )} d x

\int \frac{10}{e ^{\frac{x}{2}}} d x

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