What is the derivative of sqrt(2^x) ?

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

What is the first derivative of sqrt(2^x) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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