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Popular >

derivative of e^{x/2} 1/2

Solution

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

Solution

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

Solution steps

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

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Frequently Asked Questions (FAQ)

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