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Popular Calculus >

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

Solution

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

Solution

\frac{- x + 4}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot x ^{2} - 2 x ( x - 2 )}{( x ^{2} ) ^{2}} : \frac{- x + 4}{x ^{3}}

= \frac{- x + 4}{x ^{3}}

Graph

Popular Examples

integral of-10cos(-2x+7)

\int - 10 cos (- 2 x + 7) d x

derivative of f(x)=sin(sin(x))

d er i v a t i v e f (x) = sin (sin (x))

x^{2} d x = y^{3} d y

derivative of log_{e}(3x^2+7)

\frac{d}{d x} (lo g_{e} (3 x^{2} + 7))

integral of sin^3(x)cos^{-2}(x)

\int sin^{3} (x) cos^{- 2} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (x-2/(x^2)) ?
The derivative of (x-2/(x^2)) is (-x+4)/(x^3)
What is the first derivative of (x-2/(x^2)) ?
The first derivative of (x-2/(x^2)) is (-x+4)/(x^3)