What is the derivative of \sqrt[6]{x}-9/x ?

The derivative of \sqrt[6]{x}-9/x is (x^2+54x^{5/6})/(6x^{17/6)}

What is the first derivative of \sqrt[6]{x}-9/x ?

The first derivative of \sqrt[6]{x}-9/x is (x^2+54x^{5/6})/(6x^{17/6)}

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\frac{x ^{2} + 54 x ^{\frac{5}{6}}}{6 x ^{\frac{17}{6}}}

Solution steps

Apply the Sum/Difference Rule:

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

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= \frac{1}{6 x ^{\frac{5}{6}}} - (- \frac{9}{x ^{2}})

Simplify

\frac{1}{6 x ^{\frac{5}{6}}} - (- \frac{9}{x ^{2}}) : \frac{x ^{2} + 54 x ^{\frac{5}{6}}}{6 x ^{\frac{17}{6}}}

= \frac{x ^{2} + 54 x ^{\frac{5}{6}}}{6 x ^{\frac{17}{6}}}

3 e^{2 x} (\frac{d y}{d x}) = - 4 (\frac{x}{y ^{2}})

4 y^{^{''}} + 26 y = 0

y = 5 x

\int (3 x^{2} - 6 x - 7) d x

What is the derivative of \sqrt[6]{x}-9/x ?
The derivative of \sqrt[6]{x}-9/x is (x^2+54x^{5/6})/(6x^{17/6)}
What is the first derivative of \sqrt[6]{x}-9/x ?
The first derivative of \sqrt[6]{x}-9/x is (x^2+54x^{5/6})/(6x^{17/6)}