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Popular Calculus >

derivative of 3^{sqrt(x)}

Solution

\frac{d}{d x} (3^{x})

Solution

\frac{ln ( 3 ) \cdot 3 ^{x}}{2 x}

Solution steps

\frac{d}{d x} (3^{x})

Apply exponent rule:

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

3^{x} = e^{x l n (3)}

= \frac{d}{d x} (e^{x l n (3)})

Apply the chain rule:

e^{x l n (3)} \frac{d}{d x} (x ln (3))

= e^{x l n (3)} \frac{d}{d x} (x ln (3))

\frac{d}{d x} (x ln (3)) = \frac{ln ( 3 )}{2 x}

= e^{x l n (3)} \frac{ln ( 3 )}{2 x}

Simplify

e^{x l n (3)} \frac{ln ( 3 )}{2 x} : \frac{ln ( 3 ) \cdot 3 ^{x}}{2 x}

= \frac{ln ( 3 ) \cdot 3 ^{x}}{2 x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 3^{sqrt(x)} ?
The derivative of 3^{sqrt(x)} is (ln(3)*3^{sqrt(x)})/(2sqrt(x))
What is the first derivative of 3^{sqrt(x)} ?
The first derivative of 3^{sqrt(x)} is (ln(3)*3^{sqrt(x)})/(2sqrt(x))