What is the derivative of \sqrt[4]{1+x} ?

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

What is the first derivative of \sqrt[4]{1+x} ?

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

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\frac{1}{4 ( 1 + x ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

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

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

\frac{d}{d x} (1 + x) = 1

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

Simplify

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

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