What is the derivative of csc^3(2x) ?

The derivative of csc^3(2x) is -6csc^3(2x)cot(2x)

What is the first derivative of csc^3(2x) ?

The first derivative of csc^3(2x) is -6csc^3(2x)cot(2x)

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

- 6 csc^{3} (2 x) cot (2 x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

= 3 (csc (2 x))^{2} (- cot (2 x) csc (2 x) \cdot 2)

Simplify

3 csc^{2} (2 x) (- cot (2 x) csc (2 x) \cdot 2) : - 6 csc^{3} (2 x) cot (2 x)

= - 6 csc^{3} (2 x) cot (2 x)

What is the derivative of csc^3(2x) ?
The derivative of csc^3(2x) is -6csc^3(2x)cot(2x)
What is the first derivative of csc^3(2x) ?
The first derivative of csc^3(2x) is -6csc^3(2x)cot(2x)