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

The derivative of \sqrt[5]{3x} is (3^{1/5})/(5x^{4/5)}

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

The first derivative of \sqrt[5]{3x} is (3^{1/5})/(5x^{4/5)}

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

Solution steps

Apply the chain rule:

\frac{1}{5 ( 3 x ) ^{\frac{4}{5}}} \frac{d}{d x} (3 x)

= \frac{1}{5 ( 3 x ) ^{\frac{4}{5}}} \frac{d}{d x} (3 x)

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

= \frac{1}{5 ( 3 x ) ^{\frac{4}{5}}} \cdot 3

Simplify

\frac{1}{5 ( 3 x ) ^{\frac{4}{5}}} \cdot 3 : \frac{3 ^{\frac{1}{5}}}{5 x ^{\frac{4}{5}}}

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

\int 8 x^{- 9} d x

\int sin (2 θ) d θ

f (s) = \frac{1}{s ( s - 3 )}

\frac{d}{d x} (arccot (2 x))

x \to 1 + lim (\frac{x + 10}{x + 3})

What is the derivative of \sqrt[5]{3x} ?
The derivative of \sqrt[5]{3x} is (3^{1/5})/(5x^{4/5)}
What is the first derivative of \sqrt[5]{3x} ?
The first derivative of \sqrt[5]{3x} is (3^{1/5})/(5x^{4/5)}