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Popular >

derivative of 1/(sqrt(x^4))

Solution

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

Solution

- \frac{2}{x ^{3}}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{1}{2 ( x ^{4} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{4})

= - \frac{1}{2 ( x ^{4} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{4})

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

= - \frac{1}{2 ( x ^{4} ) ^{\frac{3}{2}}} \cdot 4 x^{3}

Simplify

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

= - \frac{2}{x ^{3}}

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\frac{\partial}{\partial x} (6 x - 4 y)

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\int (8 + x^{2}) d x

Frequently Asked Questions (FAQ)

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