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Popular Calculus >

derivative of (sqrt(x)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

Graph

Popular Examples

(\partial)/(\partial x)(35e^{5x}y)

\frac{\partial}{\partial x} (35 e^{5 x} y)

integral of x^{2/7}

\int x^{\frac{2}{7}} d x

integral of cos(-x)

\int cos (- x) d x

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

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

(\partial)/(\partial y)(2x^4y-1)

\frac{\partial}{\partial y} (2 x^{4} y - 1)

Frequently Asked Questions (FAQ)

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