What is the derivative of-(48)/(s^5) ?

The derivative of-(48)/(s^5) is (240)/(s^6)

What is the first derivative of-(48)/(s^5) ?

The first derivative of-(48)/(s^5) is (240)/(s^6)

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derivative of

- \frac{48}{s ^{5}}

\frac{240}{s ^{6}}

Solution steps

\frac{d}{d s} (- \frac{48}{s ^{5}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 48 \frac{d}{d s} (\frac{1}{s ^{5}})

Apply exponent rule:

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

= - 48 \frac{d}{d s} (s^{- 5})

Apply the Power Rule:

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

= - 48 (- 5 s^{- 5 - 1})

Simplify

- 48 (- 5 s^{- 5 - 1}) : \frac{240}{s ^{6}}

= \frac{240}{s ^{6}}

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y^{^{''}} - 0.2 y^{^{'}} + 0.01 y = 0, y (0) = 13, y^{^{'}} (0) = b

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What is the derivative of-(48)/(s^5) ?
The derivative of-(48)/(s^5) is (240)/(s^6)
What is the first derivative of-(48)/(s^5) ?
The first derivative of-(48)/(s^5) is (240)/(s^6)