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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (csc (3 - x)) = cot (3 - x) csc (3 - x)

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

Simplify

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

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

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