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Popular >

derivative of-3x^{-2/3}+4cot(x)

Solution

\frac{d}{d x} (- 3 x^{- \frac{2}{3}} + 4 cot (x))

Solution

\frac{2}{x ^{\frac{5}{3}}} - 4 csc^{2} (x)

Solution steps

\frac{d}{d x} (- 3 x^{- \frac{2}{3}} + 4 cot (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (3 x^{- \frac{2}{3}}) + \frac{d}{d x} (4 cot (x))

\frac{d}{d x} (3 x^{- \frac{2}{3}}) = - \frac{2}{x ^{\frac{5}{3}}}

\frac{d}{d x} (4 cot (x)) = - 4 csc^{2} (x)

= - (- \frac{2}{x ^{\frac{5}{3}}}) - 4 csc^{2} (x)

Simplify

= \frac{2}{x ^{\frac{5}{3}}} - 4 csc^{2} (x)

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Frequently Asked Questions (FAQ)

What is the derivative of-3x^{-2/3}+4cot(x) ?
The derivative of-3x^{-2/3}+4cot(x) is 2/(x^{5/3)}-4csc^2(x)
What is the first derivative of-3x^{-2/3}+4cot(x) ?
The first derivative of-3x^{-2/3}+4cot(x) is 2/(x^{5/3)}-4csc^2(x)