What is the derivative of arccsc(-9t^2) ?

The derivative of arccsc(-9t^2) is (2t)/(sqrt(t^4)\sqrt{81t^4-1)}

What is the first derivative of arccsc(-9t^2) ?

The first derivative of arccsc(-9t^2) is (2t)/(sqrt(t^4)\sqrt{81t^4-1)}

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derivative of

arccsc (- 9 t^{2})

\frac{2 t}{t ^{4} 81 t ^{4} - 1}

Solution steps

\frac{d}{d t} (arccsc (- 9 t^{2}))

Apply the chain rule:

- \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} \frac{d}{d t} (- 9 t^{2})

= - \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} \frac{d}{d t} (- 9 t^{2})

\frac{d}{d t} (- 9 t^{2}) = - 18 t

= - \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} (- 18 t)

Simplify

- \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} (- 18 t) : \frac{2 t}{t ^{4} 81 t ^{4} - 1}

= \frac{2 t}{t ^{4} 81 t ^{4} - 1}

What is the derivative of arccsc(-9t^2) ?
The derivative of arccsc(-9t^2) is (2t)/(sqrt(t^4)\sqrt{81t^4-1)}
What is the first derivative of arccsc(-9t^2) ?
The first derivative of arccsc(-9t^2) is (2t)/(sqrt(t^4)\sqrt{81t^4-1)}