What is the derivative of (1+x^4)^{4/5} ?

The derivative of (1+x^4)^{4/5} is (16x^3)/(5(1+x^4)^{1/5)}

What is the first derivative of (1+x^4)^{4/5} ?

The first derivative of (1+x^4)^{4/5} is (16x^3)/(5(1+x^4)^{1/5)}

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derivative of

(1 + x^{4})^{\frac{4}{5}}

\frac{16 x ^{3}}{5 ( 1 + x ^{4} ) ^{\frac{1}{5}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{4}{5 ( 1 + x ^{4} ) ^{\frac{1}{5}}} \cdot 4 x^{3} : \frac{16 x ^{3}}{5 ( 1 + x ^{4} ) ^{\frac{1}{5}}}

= \frac{16 x ^{3}}{5 ( 1 + x ^{4} ) ^{\frac{1}{5}}}

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What is the derivative of (1+x^4)^{4/5} ?
The derivative of (1+x^4)^{4/5} is (16x^3)/(5(1+x^4)^{1/5)}
What is the first derivative of (1+x^4)^{4/5} ?
The first derivative of (1+x^4)^{4/5} is (16x^3)/(5(1+x^4)^{1/5)}