What is the derivative of 3x^{-5/3} ?

The derivative of 3x^{-5/3} is -5/(x^{8/3)}

What is the first derivative of 3x^{-5/3} ?

The first derivative of 3x^{-5/3} is -5/(x^{8/3)}

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

- \frac{5}{x ^{\frac{8}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3 (- \frac{5}{3} x^{- \frac{5}{3} - 1})

Simplify

3 (- \frac{5}{3} x^{- \frac{5}{3} - 1}) : - \frac{5}{x ^{\frac{8}{3}}}

= - \frac{5}{x ^{\frac{8}{3}}}

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

\frac{d}{d x} (a cos (7 x) + b sin (7 x))

n = 1 \sum \infty \frac{2 ^{- n}}{5 ^{- n}}

\frac{d}{d x} (5 x + 3)

t^{2} e^{t}

What is the derivative of 3x^{-5/3} ?
The derivative of 3x^{-5/3} is -5/(x^{8/3)}
What is the first derivative of 3x^{-5/3} ?
The first derivative of 3x^{-5/3} is -5/(x^{8/3)}