What is the first d/(du)(u^{-1}) ?

The first d/(du)(u^{-1}) is -1/(u^2)

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d/(du)(u^{-1})

\frac{d}{d u} (u^{- 1})

- \frac{1}{u ^{2}}

Solution steps

\frac{d}{d u} (u^{- 1})

Apply the Power Rule:

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

= - 1 \cdot u^{- 1 - 1}

Simplify

- 1 \cdot u^{- 1 - 1} : - \frac{1}{u ^{2}}

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

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

\int x sin (11 - x) d x

d er i v a t i v e f (x) = x^{2} (3 + x)^{- 5}

\frac{d}{d t} (e^{t} (cos (t) - sin (t)))

y^{^{''}} + \frac{1}{4} y = 0, y (π) = 1, y^{^{'}} (π) = - 3