What is the derivative of 1/s ?

The derivative of 1/s is -1/(s^2)

What is the first derivative of 1/s ?

The first derivative of 1/s is -1/(s^2)

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derivative of

\frac{1}{s}

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

Solution steps

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

Apply exponent rule:

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

= \frac{d}{d s} (s^{- 1})

Apply the Power Rule:

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

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

Simplify

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

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

y = 27 - x^{2}, y = 6 x, y = \frac{2}{5} x

sin (3 x)

\frac{d y}{d x} = 3 x (x - 1)

x \to 0 lim (3 x^{3} + 6 x^{2} + 7 x)

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