What is the derivative of-3/4 x^{-2/3} ?

The derivative of-3/4 x^{-2/3} is 1/(2x^{5/3)}

What is the first derivative of-3/4 x^{-2/3} ?

The first derivative of-3/4 x^{-2/3} is 1/(2x^{5/3)}

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

\frac{1}{2 x ^{\frac{5}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= - \frac{3}{4} (- \frac{2}{3} x^{- \frac{2}{3} - 1})

Simplify

- \frac{3}{4} (- \frac{2}{3} x^{- \frac{2}{3} - 1}) : \frac{1}{2 x ^{\frac{5}{3}}}

= \frac{1}{2 x ^{\frac{5}{3}}}

\int \frac{7}{4 x ^{3}} d x

t y^{^{'}} - y = \frac{- t ^{3}}{y ^{2}}, y (1) = 2

\int_{0}^{3} (3 t - 5) d t

n = 1 \sum \infty n^{2} e^{n^{3}}

(\frac{x + 2}{x - 2})^{2}

What is the derivative of-3/4 x^{-2/3} ?
The derivative of-3/4 x^{-2/3} is 1/(2x^{5/3)}
What is the first derivative of-3/4 x^{-2/3} ?
The first derivative of-3/4 x^{-2/3} is 1/(2x^{5/3)}