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

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

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(\partial)/(\partial t)(x/t)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int_{0}^{3} π (9 x^{2} - x^{4}) d x

x \to 1 lim (e^{6 x^{5} - 6 x})

\int - \frac{17}{x ^{18}} d x

y = f (u) = u (y, x)^{3} - 4 y u (y, x) = g (x) = x^{3} + 3

f (x) = x^{2} - 2, at x = - 5, 23

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