What is the derivative of 2\sqrt[3]{x}-7/(sqrt(x)) ?

The derivative of 2\sqrt[3]{x}-7/(sqrt(x)) is 2/(3x^{2/3)}+7/(2x^{3/2)}

What is the first derivative of 2\sqrt[3]{x}-7/(sqrt(x)) ?

The first derivative of 2\sqrt[3]{x}-7/(sqrt(x)) is 2/(3x^{2/3)}+7/(2x^{3/2)}

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\frac{2}{3 x ^{\frac{2}{3}}} + \frac{7}{2 x ^{\frac{3}{2}}}

Solution steps

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{2 x ^{\frac{3}{2}}}

= \frac{2}{3 x ^{\frac{2}{3}}} - (- \frac{7}{2 x ^{\frac{3}{2}}})

Simplify

= \frac{2}{3 x ^{\frac{2}{3}}} + \frac{7}{2 x ^{\frac{3}{2}}}

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What is the derivative of 2\sqrt[3]{x}-7/(sqrt(x)) ?
The derivative of 2\sqrt[3]{x}-7/(sqrt(x)) is 2/(3x^{2/3)}+7/(2x^{3/2)}
What is the first derivative of 2\sqrt[3]{x}-7/(sqrt(x)) ?
The first derivative of 2\sqrt[3]{x}-7/(sqrt(x)) is 2/(3x^{2/3)}+7/(2x^{3/2)}