What is the derivative of \sqrt[4]{7x} ?

The derivative of \sqrt[4]{7x} is (7^{1/4})/(4x^{3/4)}

What is the first derivative of \sqrt[4]{7x} ?

The first derivative of \sqrt[4]{7x} is (7^{1/4})/(4x^{3/4)}

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\frac{7 ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( 7 x ) ^{\frac{3}{4}}} \frac{d}{d x} (7 x)

= \frac{1}{4 ( 7 x ) ^{\frac{3}{4}}} \frac{d}{d x} (7 x)

\frac{d}{d x} (7 x) = 7

= \frac{1}{4 ( 7 x ) ^{\frac{3}{4}}} \cdot 7

Simplify

\frac{1}{4 ( 7 x ) ^{\frac{3}{4}}} \cdot 7 : \frac{7 ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

= \frac{7 ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

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What is the derivative of \sqrt[4]{7x} ?
The derivative of \sqrt[4]{7x} is (7^{1/4})/(4x^{3/4)}
What is the first derivative of \sqrt[4]{7x} ?
The first derivative of \sqrt[4]{7x} is (7^{1/4})/(4x^{3/4)}