What is the derivative of arccsc(4x) ?

The derivative of arccsc(4x) is -1/(xsqrt(16x^2-1))

What is the first derivative of arccsc(4x) ?

The first derivative of arccsc(4x) is -1/(xsqrt(16x^2-1))

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\frac{d}{d x} (arccsc (4 x))

- \frac{1}{x 16 x ^{2} - 1}

Solution steps

\frac{d}{d x} (arccsc (4 x))

Apply the chain rule:

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

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

\frac{d}{d x} (4 x) = 4

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

Simplify

- \frac{1}{( 4 x ) ^{2} ( 4 x ) ^{2} - 1} \cdot 4 : - \frac{1}{x 16 x ^{2} - 1}

= - \frac{1}{x 16 x ^{2} - 1}

\frac{d}{d x} (1000 x - x^{2})

(\frac{x}{2})^{^{'}}

\int 5 x^{2} sin (9 x) d x

2 x, [1, 2]

\int 25

What is the derivative of arccsc(4x) ?
The derivative of arccsc(4x) is -1/(xsqrt(16x^2-1))
What is the first derivative of arccsc(4x) ?
The first derivative of arccsc(4x) is -1/(xsqrt(16x^2-1))