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Popular >

derivative of | 1/x |

Solution

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

Solution

- \frac{∣ x ∣}{x ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{∣ x ∣}{x ^{3}}

Popular Examples

integral of x(x+2)

\int x (x + 2) d x

integral from 0 to 1 of 6^{3x}

\int_{0}^{1} 6^{3 x} d x

integral of (sqrt(x^2-49))/(x^3)

\int \frac{x ^{2} - 49}{x ^{3}} d x

(\partial)/(\partial x)(4xye^x)

\frac{\partial}{\partial x} (4 x y e^{x})

limit as x approaches 2 of 3x^4+2x^2-x+1

x \to 2 lim (3 x^{4} + 2 x^{2} - x + 1)

Frequently Asked Questions (FAQ)

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