What is the derivative of $5^{\frac{x}{6}}$ $5^(x/6)$ ?

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Answer 1 · 2016-05-13T16:40:39

$= (\frac{log 5}{6}) 5^{\frac{x}{6}}$ $=((log 5)/6)5^(x/6)$

Use $a^{k x} = e^{x k log a}$ $a^(kx)=e^(x k log a)$ and $(e^(bx))'=be^(bx)$ .

$(5^(x/6))'$

$=(e^(((log 5)/6)x))'$

$=((log 5)/6)(e^(((log 5)/6)x))$

$=((log 5)/6)5^(x/6)$

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