What is (\partial)/(\partial w)(te^{w/t}) ?

The answer to (\partial)/(\partial w)(te^{w/t}) is e^{w/t}

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(\partial)/(\partial w)(te^{w/t})

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

e^{\frac{w}{t}}

Solution steps

\frac{\partial}{\partial w} (t e^{\frac{w}{t}})

Treat

t

as a constant

Take the constant out:

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

= t \frac{\partial}{\partial w} (e^{\frac{w}{t}})

Apply the chain rule:

e^{\frac{w}{t}} \frac{\partial}{\partial w} (\frac{w}{t})

= e^{\frac{w}{t}} \frac{\partial}{\partial w} (\frac{w}{t})

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

= t e^{\frac{w}{t}} \frac{1}{t}

Simplify

t e^{\frac{w}{t}} \frac{1}{t} : e^{\frac{w}{t}}

= e^{\frac{w}{t}}

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What is (\partial)/(\partial w)(te^{w/t}) ?
The answer to (\partial)/(\partial w)(te^{w/t}) is e^{w/t}