What is the derivative of arccsc(3x) ?

The derivative of arccsc(3x) is -1/(xsqrt(9x^2-1))

What is the first derivative of arccsc(3x) ?

The first derivative of arccsc(3x) is -1/(xsqrt(9x^2-1))

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\frac{d}{d x} (arccsc (3 x))

- \frac{1}{x 9 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arccsc (3 x))

Apply the chain rule:

- \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \frac{d}{d x} (3 x)

= - \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = 3

= - \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3

Simplify

- \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3 : - \frac{1}{x 9 x ^{2} - 1}

= - \frac{1}{x 9 x ^{2} - 1}

What is the derivative of arccsc(3x) ?
The derivative of arccsc(3x) is -1/(xsqrt(9x^2-1))
What is the first derivative of arccsc(3x) ?
The first derivative of arccsc(3x) is -1/(xsqrt(9x^2-1))