What is (\partial)/(\partial s)(t/s) ?

The answer to (\partial)/(\partial s)(t/s) is -t/(s^2)

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(\partial)/(\partial s)(t/s)

\frac{\partial}{\partial s} (\frac{t}{s})

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

Solution steps

\frac{\partial}{\partial s} (\frac{t}{s})

Treat

t

as a constant

Take the constant out:

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

= t \frac{\partial}{\partial s} (\frac{1}{s})

Apply exponent rule:

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

= t \frac{\partial}{\partial s} (s^{- 1})

Apply the Power Rule:

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

= t (- 1 \cdot s^{- 1 - 1})

Simplify

t (- 1 \cdot s^{- 1 - 1}) : - \frac{t}{s ^{2}}

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

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What is (\partial)/(\partial s)(t/s) ?
The answer to (\partial)/(\partial s)(t/s) is -t/(s^2)