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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int x^{- 1} + sin (x) + e^{x} d x

\frac{d y}{d x} + 2 x y = 1

h \to 0 - lim (\frac{- ln ( 1 + 6 h )}{h})

2 t^{3}

\int \frac{2}{cos ( 2 x )} d x

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