What is the derivative of arccsc(x^2+1) ?

The derivative of arccsc(x^2+1) is -2/((x^2+1)sqrt(x^2+2))

What is the first derivative of arccsc(x^2+1) ?

The first derivative of arccsc(x^2+1) is -2/((x^2+1)sqrt(x^2+2))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

- 5 sin (5 t)

\frac{d ^{2}}{d x ^{2}} (x^{- \frac{1}{11}})

\int u (x) d x

e^{5 x^{2}}

\frac{d}{d x} (ln (4 x + 3))

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