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

The derivative of \sqrt[3]{x}-5/x is (x^2+15x^{2/3})/(3x^{8/3)}

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

The first derivative of \sqrt[3]{x}-5/x is (x^2+15x^{2/3})/(3x^{8/3)}

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

\frac{x ^{2} + 15 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

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

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} - (- \frac{5}{x ^{2}}) : \frac{x ^{2} + 15 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

= \frac{x ^{2} + 15 x ^{\frac{2}{3}}}{3 x ^{\frac{8}{3}}}

y = \frac{1}{2} x^{2}, 2 x

\frac{d}{d x} (5 cos (2 x))

x \to b lim (\frac{x ^{2}}{2})

\frac{d x}{d y}, x y = 2

(1 + ln (x) + \frac{y}{x}) d x = (5 - ln (x)) d y

What is the derivative of \sqrt[3]{x}-5/x ?
The derivative of \sqrt[3]{x}-5/x is (x^2+15x^{2/3})/(3x^{8/3)}
What is the first derivative of \sqrt[3]{x}-5/x ?
The first derivative of \sqrt[3]{x}-5/x is (x^2+15x^{2/3})/(3x^{8/3)}