What is the derivative of sqrt(1+x^4) ?

The derivative of sqrt(1+x^4) is (2x^3)/(sqrt(1+x^4))

What is the first derivative of sqrt(1+x^4) ?

The first derivative of sqrt(1+x^4) is (2x^3)/(sqrt(1+x^4))

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

\frac{2 x ^{3}}{1 + x ^{4}}

Solution steps

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

Apply the chain rule:

\frac{1}{2 1 + x ^{4}} \frac{d}{d x} (1 + x^{4})

= \frac{1}{2 1 + x ^{4}} \frac{d}{d x} (1 + x^{4})

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

= \frac{1}{2 1 + x ^{4}} \cdot 4 x^{3}

Simplify

\frac{1}{2 1 + x ^{4}} \cdot 4 x^{3} : \frac{2 x ^{3}}{1 + x ^{4}}

= \frac{2 x ^{3}}{1 + x ^{4}}

What is the derivative of sqrt(1+x^4) ?
The derivative of sqrt(1+x^4) is (2x^3)/(sqrt(1+x^4))
What is the first derivative of sqrt(1+x^4) ?
The first derivative of sqrt(1+x^4) is (2x^3)/(sqrt(1+x^4))