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Popular Calculus >

derivative of 6^{sqrt(x)}

Solution

\frac{d}{d x} (6^{x})

Solution

\frac{ln ( 6 ) \cdot 3 ^{x} \cdot 2 ^{x - 1}}{x}

Solution steps

\frac{d}{d x} (6^{x})

Apply exponent rule:

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

6^{x} = e^{x l n (6)}

= \frac{d}{d x} (e^{x l n (6)})

Apply the chain rule:

e^{x l n (6)} \frac{d}{d x} (x ln (6))

= e^{x l n (6)} \frac{d}{d x} (x ln (6))

\frac{d}{d x} (x ln (6)) = \frac{ln ( 6 )}{2 x}

= e^{x l n (6)} \frac{ln ( 6 )}{2 x}

Simplify

e^{x l n (6)} \frac{ln ( 6 )}{2 x} : \frac{ln ( 6 ) \cdot 3 ^{x} \cdot 2 ^{x - 1}}{x}

= \frac{ln ( 6 ) \cdot 3 ^{x} \cdot 2 ^{x - 1}}{x}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 6^{sqrt(x)} ?
The derivative of 6^{sqrt(x)} is (ln(6)*3^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))
What is the first derivative of 6^{sqrt(x)} ?
The first derivative of 6^{sqrt(x)} is (ln(6)*3^{sqrt(x)}*2^{sqrt(x)-1})/(sqrt(x))