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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = \frac{7}{x}

\frac{\partial}{\partial x} (x^{2} (x - 2)^{4})

x^{2} y^{^{''}} + 3 x y^{^{'}} - 3 y = 0, y (1) = 0, y^{^{'}} (1) = 5

\int_{0}^{\frac{π}{4}} x sin (12 x) d x

\int \frac{4}{3 x ^{2}} d x

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