What is the derivative of 1/(sin^2(3x)) ?

The derivative of 1/(sin^2(3x)) is -6csc^2(3x)cot(3x)

What is the first derivative of 1/(sin^2(3x)) ?

The first derivative of 1/(sin^2(3x)) is -6csc^2(3x)cot(3x)

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derivative of

\frac{1}{sin ^{2} ( 3 x )}

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

Solution steps

\frac{d}{d x} (\frac{1}{sin ^{2} ( 3 x )})

Simplify

\frac{1}{sin ^{2} ( 3 x )} : csc^{2} (3 x)

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

Apply the chain rule:

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

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

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

= 2 csc (3 x) (- cot (3 x) csc (3 x) \cdot 3)

Simplify

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

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

y = 8 x - 5

5 x^{4} + 8

ln^{2} (x^{3}) - 3

(x^{2} + 2 x)^{\frac{1}{2}}

2 x^{2} + x + 5

What is the derivative of 1/(sin^2(3x)) ?
The derivative of 1/(sin^2(3x)) is -6csc^2(3x)cot(3x)
What is the first derivative of 1/(sin^2(3x)) ?
The first derivative of 1/(sin^2(3x)) is -6csc^2(3x)cot(3x)