What is the d/(ds)(1/(s^2)) ?

The d/(ds)(1/(s^2)) is -2/(s^3)

What is the first d/(ds)(1/(s^2)) ?

The first d/(ds)(1/(s^2)) is -2/(s^3)

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\frac{d}{d s} (\frac{1}{s ^{2}})

- \frac{2}{s ^{3}}

Solution steps

\frac{d}{d s} (\frac{1}{s ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

= - 2 s^{- 2 - 1}

Simplify

- 2 s^{- 2 - 1} : - \frac{2}{s ^{3}}

= - \frac{2}{s ^{3}}

4 x^{- \frac{1}{8}}

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

\frac{d y}{d x} = \frac{( 2 y + 5 ) ^{2}}{( 8 x + 9 ) ^{2}}

y = x^{2}, (2, 4)