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Popular >

derivative of sqrt(1/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 \frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 1+of (x^2)/(|1-x|)

x \to 1 + lim (\frac{x ^{2}}{∣ 1 - x ∣})

integral from 0 to pi of cos(θ)

\int_{0}^{π} cos (θ) d θ

d/(da)(a^5+a^2b^3-a^3b^2-b^5)

\frac{d}{d a} (a^{5} + a^{2} b^{3} - a^{3} b^{2} - b^{5})

integral of 2/5 x^{5/2}

\int \frac{2}{5} x^{\frac{5}{2}} d x

(dx)/(dt)=4x-x^3

\frac{d x}{d t} = 4 x - x^{3}

Frequently Asked Questions (FAQ)

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