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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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