What is the derivative of (-10/(\sqrt[3]{x)}) ?

The derivative of (-10/(\sqrt[3]{x)}) is (10)/(3x^{4/3)}

What is the first derivative of (-10/(\sqrt[3]{x)}) ?

The first derivative of (-10/(\sqrt[3]{x)}) is (10)/(3x^{4/3)}

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\frac{10}{3 x ^{\frac{4}{3}}}

Solution steps

Simplify

Take the constant out:

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

Apply exponent rule:

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

= - 10 \frac{d}{d x} (x^{- \frac{1}{3}})

Apply the Power Rule:

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

= - 10 (- \frac{1}{3} x^{- \frac{1}{3} - 1})

Simplify

- 10 (- \frac{1}{3} x^{- \frac{1}{3} - 1}) : \frac{10}{3 x ^{\frac{4}{3}}}

= \frac{10}{3 x ^{\frac{4}{3}}}

\int_{2}^{6} (\frac{1}{x - 2}) d x

x \to 1 lim (ln ∣ ln (x) ∣)

\frac{d y}{d t} = 8 y

\frac{d y}{d x} = x^{3} + 2 x + π

\int_{- 1}^{2} (- x^{2} + x + 2) d x

What is the derivative of (-10/(\sqrt[3]{x)}) ?
The derivative of (-10/(\sqrt[3]{x)}) is (10)/(3x^{4/3)}
What is the first derivative of (-10/(\sqrt[3]{x)}) ?
The first derivative of (-10/(\sqrt[3]{x)}) is (10)/(3x^{4/3)}