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Popular >

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}}}

Popular Examples

tangent of f(x)=4x^2-4x+1,(-1,8)tangent of

f (x) = 4 x^{2} - 4 x + 1, (- 1, 8)

(\partial)/(\partial x)(y-(27)/(x^2))

\frac{\partial}{\partial x} (y - \frac{27}{x ^{2}})

integral of (2sin(x)-5e^x)

\int (2 sin (x) - 5 e^{x}) d x

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\int \frac{1}{2} sin (2 θ) d θ

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

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