What is the derivative of y=arccsc(4x) ?

The derivative of y=arccsc(4x) is -1/(sqrt(x^2)\sqrt{16x^2-1)}

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

The first derivative of y=arccsc(4x) is -1/(sqrt(x^2)\sqrt{16x^2-1)}

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derivative

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

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

What is the derivative of y=arccsc(4x) ?
The derivative of y=arccsc(4x) is -1/(sqrt(x^2)\sqrt{16x^2-1)}
What is the first derivative of y=arccsc(4x) ?
The first derivative of y=arccsc(4x) is -1/(sqrt(x^2)\sqrt{16x^2-1)}