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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

Simplify

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

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

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

(x + 8 y) y^{^{'}} = 2 x - y

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

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

\int_{0}^{8} y + 1 d y

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