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Popular >

derivative of x/(x^2)

Solution

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

Solution

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

integral of sqrt(144-x^2)

\int 144 - x^{2} d x

limit as x approaches-1 of x^3+2x^2-3x-4

x \to - 1 lim (x^{3} + 2 x^{2} - 3 x - 4)

(dy)/(dx)=(xy)^2

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

derivative of x^{(2)}sin(x)derivative of

x^{(2)} sin (x)

integral from 0 to pi/2 of sin^3(3x)

\int_{0}^{\frac{π}{2}} sin^{3} (3 x) d x

Frequently Asked Questions (FAQ)

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