What is the derivative of arccsc(4x^2+1) ?

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

What is the first derivative of arccsc(4x^2+1) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= - \frac{1}{( 4 x ^{2} + 1 ) ^{2} ( 4 x ^{2} + 1 ) ^{2} - 1} \cdot 8 x

Simplify

- \frac{1}{( 4 x ^{2} + 1 ) ^{2} ( 4 x ^{2} + 1 ) ^{2} - 1} \cdot 8 x : - \frac{4}{( 4 x ^{2} + 1 ) 4 x ^{2} + 2}

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

\int (5 x^{4} + \frac{x}{7}) d x

\frac{d y}{d x} + y + 2 cos (x) = 0

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

\frac{s}{s ^{2} + 9}

\frac{d}{d x} (\frac{2 x - 9}{x})

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