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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of (3-4x/(x^2+1))

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

limit as x approaches 1-of 2^{1/(x-1)}

x \to 1 - lim (2^{\frac{1}{x - 1}})

derivative of ln^6(x)

\frac{d}{d x} (ln^{6} (x))

derivative of θsin(θ)derivative of

θ sin (θ)

(dy)/(dx)+7y-2e^{-x}=0

\frac{d y}{d x} + 7 y - 2 e^{- x} = 0

Frequently Asked Questions (FAQ)

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