What is the derivative of (x^{6/7}/5) ?

The derivative of (x^{6/7}/5) is 6/(35x^{1/7)}

What is the first derivative of (x^{6/7}/5) ?

The first derivative of (x^{6/7}/5) is 6/(35x^{1/7)}

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\frac{d}{d x} (\frac{x ^{\frac{6}{7}}}{5})

\frac{6}{35 x ^{\frac{1}{7}}}

Solution steps

\frac{d}{d x} (\frac{x ^{\frac{6}{7}}}{5})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (x^{\frac{6}{7}})

Apply the Power Rule:

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

= \frac{1}{5} \cdot \frac{6}{7} x^{\frac{6}{7} - 1}

Simplify

\frac{1}{5} \cdot \frac{6}{7} x^{\frac{6}{7} - 1} : \frac{6}{35 x ^{\frac{1}{7}}}

= \frac{6}{35 x ^{\frac{1}{7}}}

What is the derivative of (x^{6/7}/5) ?
The derivative of (x^{6/7}/5) is 6/(35x^{1/7)}
What is the first derivative of (x^{6/7}/5) ?
The first derivative of (x^{6/7}/5) is 6/(35x^{1/7)}