What is the derivative of 1/2 e^{1/2 x} ?

The derivative of 1/2 e^{1/2 x} is 1/4 e^{x/2}

What is the first derivative of 1/2 e^{1/2 x} ?

The first derivative of 1/2 e^{1/2 x} is 1/4 e^{x/2}

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\frac{d}{d x} (\frac{1}{2} e^{\frac{1}{2} x})

\frac{1}{4} e^{\frac{x}{2}}

Solution steps

\frac{d}{d x} (\frac{1}{2} e^{\frac{1}{2} x})

Simplify

\frac{1}{2} e^{\frac{1}{2} x} : \frac{1}{2} e^{\frac{x}{2}}

= \frac{d}{d x} (\frac{1}{2} e^{\frac{x}{2}})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (e^{\frac{x}{2}})

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2} e^{\frac{x}{2}} \frac{1}{2} : \frac{1}{4} e^{\frac{x}{2}}

= \frac{1}{4} e^{\frac{x}{2}}

What is the derivative of 1/2 e^{1/2 x} ?
The derivative of 1/2 e^{1/2 x} is 1/4 e^{x/2}
What is the first derivative of 1/2 e^{1/2 x} ?
The first derivative of 1/2 e^{1/2 x} is 1/4 e^{x/2}