What is the derivative of f(x)=(csc(3x-1))^{2/3} ?

The derivative of f(x)=(csc(3x-1))^{2/3} is -2cot(3x-1)csc^{2/3}(3x-1)

What is the first derivative of f(x)=(csc(3x-1))^{2/3} ?

The first derivative of f(x)=(csc(3x-1))^{2/3} is -2cot(3x-1)csc^{2/3}(3x-1)

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derivative of

f (x) = (csc (3 x - 1))^{\frac{2}{3}}

- 2 cot (3 x - 1) csc^{\frac{2}{3}} (3 x - 1)

Solution steps

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

Apply the chain rule:

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

= \frac{2}{3 ( csc ( 3 x - 1 ) ) ^{\frac{1}{3}}} \frac{d}{d x} (csc (3 x - 1))

\frac{d}{d x} (csc (3 x - 1)) = - cot (3 x - 1) csc (3 x - 1) \cdot 3

= \frac{2}{3 ( csc ( 3 x - 1 ) ) ^{\frac{1}{3}}} (- cot (3 x - 1) csc (3 x - 1) \cdot 3)

Simplify

\frac{2}{3 csc ^{\frac{1}{3}} ( 3 x - 1 )} (- cot (3 x - 1) csc (3 x - 1) \cdot 3) : - 2 cot (3 x - 1) csc^{\frac{2}{3}} (3 x - 1)

= - 2 cot (3 x - 1) csc^{\frac{2}{3}} (3 x - 1)

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

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{7}})

x \to 3 lim (\frac{x + 4}{x + 7})

\int_{0}^{1} (x^{2} + 3 x + 4) d x

x \to - 3 lim (\frac{3 - x}{3 + x})

What is the derivative of f(x)=(csc(3x-1))^{2/3} ?
The derivative of f(x)=(csc(3x-1))^{2/3} is -2cot(3x-1)csc^{2/3}(3x-1)
What is the first derivative of f(x)=(csc(3x-1))^{2/3} ?
The first derivative of f(x)=(csc(3x-1))^{2/3} is -2cot(3x-1)csc^{2/3}(3x-1)