What is the d/(dt)(e^{t/2}) ?

The d/(dt)(e^{t/2}) is e^{t/2} 1/2

What is the first d/(dt)(e^{t/2}) ?

The first d/(dt)(e^{t/2}) is e^{t/2} 1/2

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\frac{d}{d t} (e^{\frac{t}{2}})

e^{\frac{t}{2}} \frac{1}{2}

Solution steps

\frac{d}{d t} (e^{\frac{t}{2}})

Apply the chain rule:

e^{\frac{t}{2}} \frac{d}{d t} (\frac{t}{2})

= e^{\frac{t}{2}} \frac{d}{d t} (\frac{t}{2})

\frac{d}{d t} (\frac{t}{2}) = \frac{1}{2}

= e^{\frac{t}{2}} \frac{1}{2}