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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 1 + \frac{1}{x ^{4}}} (- \frac{4}{x ^{5}})

Simplify

\frac{1}{2 1 + \frac{1}{x ^{4}}} (- \frac{4}{x ^{5}}) : - \frac{2}{x ^{3} x ^{4} + 1}

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

\frac{d}{d x} (cot (x^{2}))

cos (e^{- θ^{2}})

\int (- 9) d x

\int_{- 3}^{3} x^{- \frac{1}{3}} d x

\int_{- 1}^{2} x + 2 - x^{2} d x

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