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

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

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

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

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

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

Solution steps

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

\frac{d}{d x} (x x) = \frac{3 x}{2}

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

= \frac{\frac{3 x}{2} x ^{2} - 2 x x x}{( x ^{2} ) ^{2}}

Simplify

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

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

y^{^{'}} + 3 y = e^{- 4 t}, y (0) = 5

\frac{d}{d x} (\frac{9}{e ^{x} - e ^{- x}})

x^{2} + 3 y \frac{d y}{d x} = 0

\int_{0}^{16} \frac{1}{x} d x

y^{^{'}} = ry

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