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

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

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

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

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

Solution steps

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

Treat

s

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x \to 4 lim (2 x^{4} - x^{2} - 8 x)

\frac{\partial}{\partial x} (\frac{3}{3 x + 5 y})

6 x^{2} ln (x), 24 ln (x)

\frac{d y}{d x} = \frac{1}{2} x + 2

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