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

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

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

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

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derivative of

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

= 2 csc (x) (- cot (x) csc (x))

Simplify

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

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

\int x^{2} 9 + x d x

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

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0, y (0) = 8

\int (x + 6)^{4} d x

y = x, y = x, x = 0, x = 2

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