What is the derivative of y=(-5)/(\sqrt[3]{x)} ?

The derivative of y=(-5)/(\sqrt[3]{x)} is 5/(3x^{4/3)}

What is the first derivative of y=(-5)/(\sqrt[3]{x)} ?

The first derivative of y=(-5)/(\sqrt[3]{x)} is 5/(3x^{4/3)}

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derivative of

y = \frac{- 5}{3 x}

\frac{5}{3 x ^{\frac{4}{3}}}

Solution steps

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

Simplify

\frac{- 5}{3 x} : - \frac{5}{3 x}

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{5}{3 x ^{\frac{4}{3}}}

f (x) = 2 x^{2} - 4 x - 5, at x = 2

\int sin (e^{x}) e^{x} d x

\frac{d y}{d x} = \frac{3 y ^{2} + 10 x ^{2}}{x y}

\frac{d}{d x} (7 x - 5)

\int_{0}^{4} x^{\frac{3}{2}} d x

What is the derivative of y=(-5)/(\sqrt[3]{x)} ?
The derivative of y=(-5)/(\sqrt[3]{x)} is 5/(3x^{4/3)}
What is the first derivative of y=(-5)/(\sqrt[3]{x)} ?
The first derivative of y=(-5)/(\sqrt[3]{x)} is 5/(3x^{4/3)}