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

The derivative of 1/(2^{sqrt(x))} is -(ln(2)*2^{-sqrt(x)-1})/(sqrt(x))

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

The first derivative of 1/(2^{sqrt(x))} is -(ln(2)*2^{-sqrt(x)-1})/(sqrt(x))

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derivative of

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

- \frac{ln ( 2 ) \cdot 2 ^{- x - 1}}{x}

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{- x} = e^{(- x) l n (2)}

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

Apply the chain rule:

e^{(- x) l n (2)} \frac{d}{d x} ((- x) ln (2))

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

\frac{d}{d x} ((- x) ln (2)) = - \frac{ln ( 2 )}{2 x}

= e^{(- x) l n (2)} (- \frac{ln ( 2 )}{2 x})

Simplify

e^{(- x) l n (2)} (- \frac{ln ( 2 )}{2 x}) : - \frac{ln ( 2 ) \cdot 2 ^{- x - 1}}{x}

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

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