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

The derivative of 3/(\sqrt[3]{x}) is -1/(x^{4/3)}

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

The first derivative of 3/(\sqrt[3]{x}) is -1/(x^{4/3)}

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- \frac{1}{x ^{\frac{4}{3}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

= - \frac{1}{x ^{\frac{4}{3}}}

x \to 0 lim (\frac{sin ( x ^{3} )}{x})

\int cos^{7} (x) sin^{6} (x) d x

9 + cot^{2} (x)

x^{2} (1 - 2 x)

(1 - x) \frac{d y}{d x} - x y = x + x^{2}

What is the derivative of 3/(\sqrt[3]{x}) ?
The derivative of 3/(\sqrt[3]{x}) is -1/(x^{4/3)}
What is the first derivative of 3/(\sqrt[3]{x}) ?
The first derivative of 3/(\sqrt[3]{x}) is -1/(x^{4/3)}