What is the derivative of 3-(10/(3x^{1/6)}) ?

The derivative of 3-(10/(3x^{1/6)}) is 5/(9x^{7/6)}

What is the first derivative of 3-(10/(3x^{1/6)}) ?

The first derivative of 3-(10/(3x^{1/6)}) is 5/(9x^{7/6)}

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\frac{d}{d x} (3 - \frac{10}{3 x ^{\frac{1}{6}}})

\frac{5}{9 x ^{\frac{7}{6}}}

Solution steps

\frac{d}{d x} (3 - \frac{10}{3 x ^{\frac{1}{6}}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3) - \frac{d}{d x} (\frac{10}{3 x ^{\frac{1}{6}}})

\frac{d}{d x} (3) = 0

\frac{d}{d x} (\frac{10}{3 x ^{\frac{1}{6}}}) = - \frac{5}{9 x ^{\frac{7}{6}}}

= 0 - (- \frac{5}{9 x ^{\frac{7}{6}}})

Simplify

= \frac{5}{9 x ^{\frac{7}{6}}}

What is the derivative of 3-(10/(3x^{1/6)}) ?
The derivative of 3-(10/(3x^{1/6)}) is 5/(9x^{7/6)}
What is the first derivative of 3-(10/(3x^{1/6)}) ?
The first derivative of 3-(10/(3x^{1/6)}) is 5/(9x^{7/6)}