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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 ( e ^{x} - 2 ) ^{\frac{1}{2}}} e^{x} : \frac{e ^{x}}{2 ( e ^{x} - 2 ) ^{\frac{1}{2}}}

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

\int (x sin (2 x)) d x

\int sin (9 x) cos (3 x) d x

x \to 7 + lim (7 x - 7)

\int (4 x - 9) d x

\frac{d}{d x} (x - e)

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