What is the derivative of (sqrt(x)/(x^2)) ?

The derivative of (sqrt(x)/(x^2)) is -3/(2x^{5/2)}

What is the first derivative of (sqrt(x)/(x^2)) ?

The first derivative of (sqrt(x)/(x^2)) is -3/(2x^{5/2)}

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

- \frac{3}{2 x ^{\frac{5}{2}}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{\frac{1}{2 x} x ^{2} - 2 x x}{( x ^{2} ) ^{2}} : - \frac{3}{2 x ^{\frac{5}{2}}}

= - \frac{3}{2 x ^{\frac{5}{2}}}

y^{^{''}} - 2 y^{^{'}} + y = e^{x} ln (x)

\frac{d}{d x} (arcsin (\frac{x}{4}))

\frac{d}{d x} (tan^{4} (3 x))

\int y^{3} e^{- y} d y

\int - \frac{14}{15} \cdot (x - 30) + 14 d x

What is the derivative of (sqrt(x)/(x^2)) ?
The derivative of (sqrt(x)/(x^2)) is -3/(2x^{5/2)}
What is the first derivative of (sqrt(x)/(x^2)) ?
The first derivative of (sqrt(x)/(x^2)) is -3/(2x^{5/2)}