derivative of \sqrt[5]{3x} — step-by-step solution

⚠ 3x is read as the product 3*x: for a power, write 3^x‖A LaTeX root is read as a fractional power: write (expression)^(1/n), with n=2 for a square root

Let's differentiate:

\frac{d}{d x} ({(3 x)}^{\frac{1}{5}})

\frac{d}{d x} (3^{\frac{1}{5}} \cdot x^{\frac{1}{5}})

ℹ

\frac{d}{d x} (3^{\frac{1}{5}} \cdot x^{\frac{1}{5}})

3^{\frac{1}{5}} \cdot \frac{d}{d x} (x^{\frac{1}{5}})

‖

\frac{d}{d x} (x^{\frac{1}{5}})

\frac{1}{5} \cdot x^{(\frac{1}{5} - 1)}

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

ℹ

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

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

‖

\frac{1}{5} - 1

\frac{1 - 1 \cdot 5}{5}

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

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

\frac{3^{\frac{1}{5}} \cdot x^{- \frac{4}{5}}}{5}

\frac{3^{\frac{1}{5}}}{x^{\frac{4}{5}} \cdot 5}

▶Derivative:

\frac{3^{\frac{1}{5}}}{5 x^{\frac{4}{5}}}