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Popular >

derivative of 2^{sqrt(x)}

Solution

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

Solution

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

Solution steps

\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}

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Frequently Asked Questions (FAQ)

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