What is the derivative of \sqrt[4]{9x} ?

The derivative of \sqrt[4]{9x} is (sqrt(3))/(4x^{3/4)}

What is the first derivative of \sqrt[4]{9x} ?

The first derivative of \sqrt[4]{9x} is (sqrt(3))/(4x^{3/4)}

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

Solution steps

Apply the chain rule:

\frac{1}{4 ( 9 x ) ^{\frac{3}{4}}} \frac{d}{d x} (9 x)

= \frac{1}{4 ( 9 x ) ^{\frac{3}{4}}} \frac{d}{d x} (9 x)

\frac{d}{d x} (9 x) = 9

= \frac{1}{4 ( 9 x ) ^{\frac{3}{4}}} \cdot 9

Simplify

\frac{1}{4 ( 9 x ) ^{\frac{3}{4}}} \cdot 9 : \frac{3}{4 x ^{\frac{3}{4}}}

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

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12 arcsin (e^{\frac{x}{2}})

\frac{7 x}{8}

What is the derivative of \sqrt[4]{9x} ?
The derivative of \sqrt[4]{9x} is (sqrt(3))/(4x^{3/4)}
What is the first derivative of \sqrt[4]{9x} ?
The first derivative of \sqrt[4]{9x} is (sqrt(3))/(4x^{3/4)}