What is the derivative of f(x)=(sqrt(x))/x ?

The derivative of f(x)=(sqrt(x))/x is -1/(2x^{3/2)}

What is the first derivative of f(x)=(sqrt(x))/x ?

The first derivative of f(x)=(sqrt(x))/x is -1/(2x^{3/2)}

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derivative of

f (x) = \frac{x}{x}

- \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}}}

y^{^{'''}} - 4 y^{^{''}} + 4 y^{^{'}} = 8 x

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\int 1 - x^{3} d x

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