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}}

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