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Popular >

derivative of (x-1/(x^2))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of sqrt(x)*(7x^2+x)

\int x \cdot (7 x^{2} + x) d x

integral of sqrt(8^2-x^2)

\int 8^{2} - x^{2} d x

integral from-1 to 1 of (2x^2-x^3)

\int_{- 1}^{1} (2 x^{2} - x^{3}) d x

derivative of In(x^2+7)

\frac{d}{d x} (I n (x^{2} + 7))

integral of (x-3)/((x+8)(x-2))

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

Frequently Asked Questions (FAQ)

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