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

The derivative of (x^2+x-2/(x^2)) is (-x+4)/(x^3)

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int (\frac{x ^{3}}{3})^{'} sin (x) d x

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

d er i v a t i v e 1 + sec (2 x)

l a pl a ce t r an s f or m cos (θ)

x \to 0 lim (e^{x})

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