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Popular >

derivative of (sqrt(x))/(x^2)

Solution

derivative of

\frac{x}{x ^{2}}

Solution

- \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}}}

Popular Examples

(\partial)/(\partial x)(9/x+3/y+xy)

\frac{\partial}{\partial x} (\frac{9}{x} + \frac{3}{y} + x y)

derivative of x^{arctan(x})

\frac{d}{d x} (x^{a r c t a n (x)})

(dy)/(dx)+6(tan(6x))y=9cos(6x)

\frac{d y}{d x} + 6 (tan (6 x)) y = 9 cos (6 x)

derivative of 8x^2-x^3

\frac{d}{d x} (8 x^{2} - x^{3})

integral from 0 to x of cos(t)

\int_{0}^{x} cos (t) d t

Frequently Asked Questions (FAQ)

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)}