What is (\partial}{\partial t}(\frac{(3r+s))/t) ?

The answer to (\partial}{\partial t}(\frac{(3r+s))/t) is -(3r+s)/(t^2)

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(\partial}{\partial t}(\frac{(3r+s))/t)

\frac{\partial}{\partial t} (\frac{( 3 r + s )}{t})

- \frac{3 r + s}{t ^{2}}

Solution steps

\frac{\partial}{\partial t} (\frac{( 3 r + s )}{t})

Treat

r, s

as constants

Take the constant out:

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

= (3 r + s) \frac{\partial}{\partial t} (\frac{1}{t})

Apply exponent rule:

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

= (3 r + s) \frac{\partial}{\partial t} (t^{- 1})

Apply the Power Rule:

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

= (3 r + s) (- 1 \cdot t^{- 1 - 1})

Simplify

(3 r + s) (- 1 \cdot t^{- 1 - 1}) : - \frac{3 r + s}{t ^{2}}

= - \frac{3 r + s}{t ^{2}}

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

\frac{d}{d x} ((8 x^{2} - 2 x) (5 x + 9))

y^{^{''}} - 4 y^{^{'}} + 53 y = 0

\frac{d}{d x} ((x^{5} + 1)^{6})

x \to 5 lim (\frac{x}{x + 1})

What is (\partial}{\partial t}(\frac{(3r+s))/t) ?
The answer to (\partial}{\partial t}(\frac{(3r+s))/t) is -(3r+s)/(t^2)